Out of curiosity when did Australians start regarding themselves as Australian? ...
Well, downside, I guess a formal lower limit is 1901 - when the Commonwealth of Australia formally came into being (i.e. at Federation). Before that - from settlement/invasion in 1788 - we (officially) lived in the (British) Colony of NSW, and later there was also the (British) Colony of Victoria, etc, etc. But, well before Federation - as MarieC explained - the idea of being Australian (regardless of the official position) became very strong round the 1870s and thenceforth.
How we have regarded ourselves (and there was - and is - anything but unanimity on this), how others have regarded us, and what we have been under our Law were (and still are) far from the same!
At Federation in 1901,
‘British subject’ was the sole civic status noted in the Australian Constitution! Even up until 1969, we Australians were still officially required to declare our
nationality as British! The term ‘Australian nationality’ had no official recognition until 1969; and it wasn't until an Act of 1984 came into effect in
1987 that we ceased to be British subjects!
Our Head of State remained the Monarch of Great Britain & Northern Ireland.
Inter alia this means, I believe, that (under the UK Act of Settlement) our Head of State must be a natural legitimate descendant (and the rules of male primogeniture apply) of Sophia, Electress of Hanover (1630–1714), a granddaughter of James I (hmmm); must be a Protestant: must not be, or ever have been a Roman Catholic or have been married to a Roman Catholic; etc, etc, etc ...! Crazy stuff!
So even today, when we are just about to enter 2008, our Head of State is not an Australian

- we still have Elizabeth II as our Head of State!
Given this, one might well ask whether we even yet regard ourselves as Australian
Weird and wonderful are the ways of the world ...
JAP