What seems to work for me is improving relations with Britain, West and South Australia, and Dieman's land, and harming relations with New South Wales. Research Colonialism and then Nationalism ASAP and try to have greater GDP than any of the three you're befriending, they're really weak so it shouldn't be too hard.
Pop a colony in South Island, North Island and West Australia. I'm not sure how colony placement works exactly, it seems to go roughly where you click but I'm not 100% on that. Try to put your WA colony so it borders the rest of the state from the start.
Once Nationalism is researched, federate quickly. You should absorb West Australia first, but since they're trying to do it to, and Britain is trying to do it to them you can wind up with new territory more or less out of nowhere. Sometimes when Britain federates you with another state you come out on top, not sure what determines it because it doesn't seem to be GDP, might be number of states. Once federation starts the whole thing will finish up fast, as in everyone becoming a single nation within the space of a few months.
I think what happens when you get annexed out of nowehere is Britain gets 20 relationship with you through passive gain from the vassal relationship, and then takes a decision to federate 2 Australian states, which usually gets you swallowed by NSW. From my America runs I presume Britain's decisions to federate it's Australian subjects is similar to the ones you get for Canada, which just require the overlord to have 20 relationship with two subject states of the right cultures, and not be on the 5 year cooldown. It's still hard to predict though, and I'm genuinely not sure why it happens some runs and not others.