I would recommend "The Fatal Shore" by Robert Hughes if you are interested in reading up on the subject.

To sum up the points brought up in the book, it was difficult to get to and had almost no useful resources. It was originally thought that its pine trees and hemp would be invaluable to England's shipbuilding industry but the pine was the wrong quality and the hemp industry, needing skilled labor and not penal labor, never took off.

The early settlers had to rely heavily on imported food and goods as they had a hard time getting the land near the harbors to produce food. This was partly due to the fact that the penal laborers weren't especially motivated, but the soil was not nearly as fertile as they had hoped.

There was also talk of how important Australia could be from a naval standpoint as an outpost from which to attack French trade routes, but it was a little too far to be of much use in that regard, and the French never even bothered to settle a colony.

It was largely due to wool that Australia became economically viable, and thus worth looking into, but this didn't happen until sheep were introduced from England.

Fact is, the colonies in Australia were kept going purely for penal purposes for a very large part of its early history and were economic drains on England during that time.

EDIT: I wanted to add that "The Fatal Shore" is from England's perspective and focuses almost entirely on the activities and history of Australia. There are possibly internal reasons as well for why the other major national powers never cared much for Australia.

Josephdevon gave a good answer, and though I am no expert on the scramble for Africa, I am well versed in Australia's colonial history.

Basically, unlike the scramble for Africa, there were only really four European countries capable of colonising Australia: Portugal, The Netherlands, France, and Britain. Other countries simply lacked the established colonial network to maintain a settlement this far from Europe.

So why did only Britain colonise Australia? To look at Australia's colonisation you have to first look at the colonisation of the region. By the 16th century the Portuguese had established a presence in the East Indies. The Dutch came onto the scene in the early 17th century, and through their East India Company soon became a large and lasting power in the Malay Archipelago. In the 1640's Abel Tasman mapped much of the Australian coast, and William Dampier charted the west coast in the 1680's. When Captain James Cook mapped the east coast for the British in 1770, there was as of yet no European presence on the island continent, and there wouldn't be until 1788.

So what was the cause for this large gap between exploration and colonisation? Manning Clark puts forth the view that the lack of either exploration (in the case of the Portuguese), or colonisation (the Dutch), was related to the religious leanings of the European powers. He contends that the Portuguese explored and exploited the region for the glory of God and the pope, and saw that they could best serve the church through the spice trade rather than any further exploration toward a mysterious southern land. Clark says that The Dutch, who were Calvinist Protestants, unlike the Catholics were impelled by profit and god, rather than profit for god. Then came the enlightenment, by which time mankind had developed the world-view necessary to colonise Australia...

I won't take issue with the Enlightenment having influenced the founding of Australia, or its effect on the men of that time, but I don't believe that it was necessary for setting the colonisation in motion. Max Weber's the Protestant Ethic and the Spirit of Capitalism type arguments have their place, but I'm more inclined toward a political realism in these matter.

John Gascoigne seems to have similar views, contending that 'colonisation had been a pragmatic venture prompted by uninspiring ends', and I agree with him. The Portuguese didn't fail to chart Australia because of Catholic influence, but because expeditions are expensive and dangerous, and because at that time they had from Africa to China to choose from to build up their empire. The reasons for the lack of Dutch colonisation are similar; in Abel Tasman's instructions from the Dutch East India Company, they told him the reasons for exploration were due to the possibility of riches and treasures. When he failed to find such riches, they saw it would not be profitable to establish a presence in the regions he explored. In contrast, Morton's instructions to Cook seem to be more 'Enlightened,' calling for the humane treatment of the indigenous people, but an undercurrent of pragmatism flows through them. By the time Cook's expedition was outfitted, a benefit to the colonisation of Australia had arisen, and this benefit seemed to apply to only Britain, and, as contended by Noelene Bloomfield: France.

Bloomfield informs us that the French sent many expeditions in the late 18th and early 19th centuries to chart Australia for themselves. As well as this, the region would have been strategically important for them to hold, as they had recently lost their holdings in the Indian Ocean to the British. French settlement in Australia was not to be, however, as the Napoleonic Wars prevented them from gaining a foothold, and after the country had recovered enough to start colonising once again, the entirety of Australia had been claimed by the British. The British reasons we know well enough; to cement their presence in the region and protect the approaches to India, because of the loss of their American possessions by 1783, and due to domestic issues such as overcrowding.

So why 1788? And why was there no scramble? Because regardless of ideology, until that point there had been no compelling reasons for the colonisation of Australia to be undertaken, and there were only a handful of European countries capable of doing so.

Limited Bibliography:

-'Australia and the Enlightenment' in Deborah Gare and David Ritter (eds), Making Australian History: Perspectives on the Past since 1788, Thomson, South Melbourne, 2008, pp. 1-32.

-Gascoigne, John, The Enlightenment and the Origins of European Australia, CUP, Melbourne, 2002.

this is not my area of expertise - I have more familiarity with Africa - but in designing a Transnational course on Forced Migration I have some experience with Australia as a colony.

first, I think you're assuming quite a bit when you say that Australia is similar to Africa. just take a quick look at a map and you'll see some of the bigger differences; Africa has much less open ocean to traverse from Europe than Australia. whether through the northern Mediterranean access or by following the Italo-Spanish coasts, Africa is quite accessible (at least on the coasts). in my estimation, Australia has a lot more in common with a country like Canada, where the vast majority of the territory (the North in Canada and the deserts in Australia) is hardly suitable for colonization. Hughes' The Fatal Shore is quite useful in describing the many difficulties the British had in setting up penal colonies in Australia due to its climate, physical features, and immense territory.

now on the matter of whether Britain was unchallenged, the easy answer is definitely 'yes'. now the hard answer has much more to do with the features of the international marketplace in that period and the nature of territorial expansion as a result. it's worth noting that the Dutch East India Company (Kerry Ward's work is fantastic on this subject) was the main competitor for Britain's own imperial expansion and though it did make contact with Australia, there was little there to warrant the creation of a link in the trade network. further, those territories touching the Indian Ocean were much more important (for both the Dutch and the British). for the Dutch, the Cape Colony of South Africa was difficult enough to manage with the potential for a much higher payoff if they stayed the course (that last sentence might seem to imply they were weighing Australia but I've seen no evidence of it being a possibility for the Dutch). essentially, the only fleet that could've challenged the British (actually preempted) never fully committed to actually settling though they made periodic contact with what they called 'New Holland'.

it took almost 200 years from the first European encounter with Australia until its colonization. even when it was, Australia was seen as more of a solution to domestic problems (crime and overcrowding of jails, surplus population unable to find work, and a culture of purity that England could not live up to without solving the problem of undesirables). essentially, it just wasn't that desirable outside of its possibilities for stashing away convicts and the poor.

The French had vague notions of exploring, finding out what was here, and may have set up a colony, if fate had not scuttled them.

La Perouse was investigating the area in 1788, arriving in Port Jackson (what is now Sydney Harbour) only a few days after the first British settlement. He then sailed off to the area around the Solomon Islands and was never seen again. Some British convicts had even tried to escape aboard his ships - just as well for them they didn't succeed.

If he'd been a few years earlier, if the revolution the following year not intervened, if the British had delayed their colony's establishment by 20-30 years? Who knows what would have happened. But, of course, that was not to be.