This came up in another thread, but I've intentionally left the country out. While "whiteness" in the US is interesting, I'm really more interested in Australia.
Did migrants to the two countries have similar experiences of the changing definition of "white"? How was white defined culturally and legally, and how has it changed over time?
Sorry for the short answer, but in general, white in Australia by and large meant or British or Irish decent...
However this does change over time... There was some more tolerance of white Europeans - you'll find a lot of German place names in Australia, and the classic image of an Australian bushman is based on that of the German... But in general, British were treated the best, and it got worse the further south you went in Europe...
For instance, its common in early newspapers to read people described as Britishers, Europeans, Blacks, Chinese and Natives, et cetera... There were categories, a hierarchy of sorts...
However it shifts around at different times, the White Australia Policy is a good place to start: