Perhaps if a lot of the other surrounding British territories and colonies also all wanted independence from the British as well and then sought to join a unified Australian/New Zealander polity, such as Papua New Guinea, New Caledonia, and the Solomon Islands. It would be pretty unwieldy and power and influence would remain further on the continent. There would probably need to be some momentous, tide-changing events that would cause all these territories to band together and form a full "Australian" identity despite their cultural differences, like a foreign invasion.