With Polynesia, none. But with Indonesia, the story is very different. Macassan traders and fishermen from Sulawesi had been sailing to Arnhem Land and the Kimberley since at least the 1700s, though there's disagreement over exactly how long they've been doing this. Rock art in Arnhem land depicting Macassan vessels has been dated to at least the 1660s and perhaps as early as the 1510s. Some old camping sites associated with Macassan, distinguished by the presence of taramind - a tree brought to Australia from Indonesia by such sailors - have been dated to between 1170 and 1520 (though there is some suspicion that the older dates represent a purely Aboriginal settlement phase at the site, predating the arrival of foreign traders). A 12th Century coin from Kilwa - the dominant Swahili port in East Africa - has been found on an island off the coast of Arnhem Land. Whether it got their as part of 12th Century trade routes across the Indian Ocean or whether it was brought much later by the Portuguese who pillaged the Swahili coast on their way to the East Indies is a matter of some debate. In the oral history of the Yolngu (the people of eastern Arnhem Land), the Djanggawul Ancestors encounter a people called the Baijini who came down from the north to fish for trepang and brought tamarind with them, but were said to pre-date the Macassans, so perhaps another group arrived from Indonesia before the Macassans did.
Historically, between 60-70 Macassan vessels, with crews of about 30 men each, arrived each year in Arnhem Land. They made camp along the shore and worked with the local Yolngu to harvest and process trepang - sea cucumbers - that were then sold to the Chinese. In exchange for their assistance and the right to use their land and waters, the Yolngu received goods from the Macassans: metal tools and weapons and cloth being the main items of traded. Many Yolngu joined the Macassan crews and sailed back and forth between Indonesia and Australia, and many Macassans married into Yolngu families.
Along the coast of the Kimberley, the story is a bit different, at least historically. There the Macassans might have overstayed their welcome or otherwise ran afoul of the wunan (also spelled wurnan) - the law that governs trade relations in the Kimberley. The oral history here indicates that the people of the Kimberley felt that they had been cheated out of their due by the Macassans. By the time Europeans showed up the Macassans had to fortify their seasonal camps and were subject to raids and thefts.
There is a lot of evidence for historical contact with Indonesia, but its very hard to discern prehistoric trade/contact with Australia's surrounds (i.e. the vast majority of Australian time). One of the contributing factors for this is that in the 20th century it was popular to explain Australian technological and social developments of the last 5000 years as the result of influences from these external places like Indonesia. But from the late 80s onwards there was a backlash against this idea (because it robbed Aboriginal people of their innovation) so that today people are reluctant to talk about prehistoric trade between Australia and its surrounds.
That said, the other reason is simply that evidence is very scarce! The only definite link between Australia and the outside world is the dingo (Canis dingo), probably brought around 4000 years ago. It was most likely the Austronesians who brought the dingo, but it also possibly might have been from New Guinea via the Torres Strait.
Other possible links with New Guinea include shell fishhooks which made their way down the eastern coast in the last 1000 years, and outrigger canoes, which were restricted to Cape York in the historical period.
Trade in the historic period between Cape York and New Guinea via Torres Strait was well known and a number of goods were traded across. People in the Strait were intermediaries of trade between NG and Australia, with a major aspect being animals - domestic animals like pigs were imported (occasionally) from NG for their meat and tusks, and it has been suggested similar practices account for the importation of cuscus, cassowary, macropod and dog/dingo as either pets or sources of wild meat.
Thanks heaps