An alternate WW1 could do it, Australia make look big on a map and it is big and impressive indeed, but think populated and along the coast, with back then little industry.
Suppose Britian annoys the US just a little more during the civil war, possibly recognizing Dixie even if it doesn't directly get involved. And maybe a little annoyance over say Alaska's border and maybe a few disagreements over fishing rights here and there. Maybe they even really take the piss and put a protectorate status over Hawaii. Or block annexation, whatever.
Somehow they push themselves and the US into a kind of cold war, now the US moves closer to Germany and the central powers here.
WWI breaks out, and the US breaks out all it's industrial might and a few supprises. In the final peace the US snags up most of the big white dominions, Canada, Australia, and New Zealand.
They keep New Zealand and give Australia some sort of Commonwealth like status, meanwhile Canada becomes outright states and New Zealand too eventually.