This is rather difficult with a post-1788 point of departure.
Australia already
had a form of slave labour (okay, indentured labour): convicts. It was the reason the place was set up, after all. There's no reason to import African slaves to a colony which was set up as a convict labour camp.
By the time the transportation of convicts had stopped - in fact, even before that - the British electorate had turned vehemently anti-slavery, so establishing a formal slave trade was politically impossible.
Even after that, when some Australians did turn to unofficial slave labour, they went to a closer source: the Pacific Islands. The "blackbirders" in Queensland amounted to slavery (or close to it) when growing sugar, but there was no need to set up a trade in slaves from Africa. This would apply to just about any form of slavery in eastern Australia, since it's closer to bring slaves from the Pacific Islands.
If you have an *Australia which is settled before 1788, and by someone other than the British, it may be possible.
Here is one example of where it happened, for instance, but that's with a PoD well before 1788.