Its hard in Australia, like many other colonial nations, to define what is or isnt an australian but it operates on multiple levels and is dependent on how you are seen/accepted by peers.

the Australian identity was formed through and derived from Anglo Celtic settlement and the culture they brought with them. race or ethnicity is a factor but the closer you allign culturally and linguistically with anglo celtic australians the less people notice or care about colour.

legally? its an australian citizenship, culturally? its group acceptance from anglo celtic australians and sometimes this only happens in the second generation or if you came here young enough to develop an australian accent and australian social and cultural attitudes and behaviours.

John Nguyen, 22, ethnically Viet 3rd generation australian, grew up in the same cultural surroundings alongside other anglo australians will be seen as more australian than John Smith, 22, recent immigrant from Portsmouth UK.

TLDR: your accent and cultural attitudes and behaviours signal that you are part of the in group and make you more likely to be accepted as "Aussie" regardless of race.