I was just wondering if it were possible for the island of Australia to be settled by Polynesians.
(Assuming you mean Polynesians, not the older Lapita culture)
With aborigines? Not likely. The coast of Queensland might support Polynesian agriculture, but the Polynesians would probably not consider it worth it to sail hundreds of miles to get a spear in the spleen. Especially when there are perfectly fine uninhabited islands in the same sailing distance.
Assuming there is no human settlement in Australia before the Austronesian expansion (this was the migration from mainland Asia which eventually became the Polynesians), the Polynesians are butterflied away. Pre-Ice Age non-settlement of Australia means non-settlement of New Guinea too-that means that post-Ice Age Austronesians find virgin land in New Guinea, and probably settle there en masse instead of mixing with native New Guineans to spark the Lapita culture.
Without the Lapita culture, there is no settlement of Micronesia (where the Polynesian culture began) and no settlement of Melanesia beyond New Guinea.
These *New Guinean natives may stumble eventually on the Solomon islands and Australia, but I think they would lose a lot of their seafaring traditions on the large island of New Guinea, where they can respond to events like mass fish deaths by retreating inland for food instead of sailing outward. They colonize these near lands, with dense agricultural settlements in coastal Queensland, and hunter-gatherer bands spreading outside of this agricultural area. As per OTL, a lot of megafauna goes extinct in Australia-possibly more than OTL, as feral pigs from Asia take over the land. Unlike the Aborigines of OTL, the *Australians keep bows and arrows to hunt these pigs.
As for European colonization, it may be partially diverted to virgin land such as New Zealand in this scenario.
Actually, I think it is a good thing for pigs and chickens to be introduced early in Australia. They breed much faster
See, breed much faster=ecological collapse caused by invasive species. Now in the long run they might create butterflies that create cultures that are better able to resist colonialism, but that's not a given, and on the way to those cultures you'd get a lot of misery as the hunter-gatherer peoples struggle to adapt to an environment in flux.