You've probably seen a comic or cartoon depicting a "caveman" chipping away at a stone disk to invent the wheel. It's an iconic image in pop culture, but an erroneous one that builds upon and feeds into an idea that the wheel is a primal human technology, as basic as fire or the spear. In fact, the invention is much more recent than the pop-culture perception would have you believe and far from being a ubiquitous invention, it appears to have been developed only once (maybe twice, but the two earliest sites with wheels are so close in time and space that it likely represents a single invention).

This post from a couple months ago goes into greater detail, as does this post over at /r/BadHistory. The basics of the wheel's early history is that it first appears in eastern Europe / western Asia around 3500 BCE and spreads from there in a pattern closely linked to the spread of Proto-Indo-European speaking peoples and their domesticated horses.

That last part - regarding the simultaneous spread of domestic horses - is important. Earlier wheeled vehicles are all large and relatively cumbersome. They need powerful animals like horses and oxen to pull them. Smaller wheeled vehicles like handcarts and wheelbarrows won't show up until a couple thousand years later.

In societies that lacked powerful domestic animals to do the early heavy lifting, wheels aren't nearly as useful. In the first millenium CE, the Classical Veracruz cultures (specifically Remojadas) made wheeled figurines which are often described as "toys." While wheels of this nature can be found at other Mesoamerican sites as well, they remain a novelty item rather than the foundation of transportation technologies. If you have to rely on human labor for transportation, wheels aren't necessarily your best option.

This brings us to Australia. There were no wheeled vehicles in Australia before Europeans arrived, nor are there any wheeled artifacts like there are in Mesoamerica (at least, none found yet). Like the Americas, Australia lacks powerful domestic animals that could have pulled early wheel vehicles. Australian Aboriginal peoples did have other technologies in common with other parts of the world that aided in their ability to transport a large number of items over long distances, such as dillybags and tumplines. There was a thriving continental trade system that circulated bayer shells and other marine resources from the coasts, pituri from the interior, red and white ocher from a handful of sites scattered around the continent and stone tools from places like Mount Isa in Queensland and Mount William in Victoria, among other resources.