The state in which I grew up and currently reside, Queensland, celebrated its sesquicentennial anniversary today. 150 years ago, on 6 June 1859, Queen Victoria signed Letters Patent separating the state of Queensland from New South Wales.
Although one of my parents was not born in Australia (my mother emigrated from Switzerland with her family when she was nine years old), I've done some family history research on my father's side and the earliest Australian-born direct ancestor I've found is one of my paternal great-great grandmothers who was born in Brisbane (the future state capital) in 1855.
The area that currently forms Brisbane was originally (from 1825) the Moreton Bay penal colony, intended as a place for recidivist convicts who had offended while serving out their sentences in New South Wales. In 1839 transportation of convicts to Moreton Bay ceased and the Brisbane penal settlement was closed. In 1842 free settlement was permitted and people began to colonise the area voluntarily.
I have no indication whatsoever (unfortunately) that this particular great-great grandmother was the daughter of convicts. In Australia in the past, having an ancestor who was a convict was quite shameful, however times have changed, and these days having a convict ancestor practically means that you are 'Australian Royalty'. ;)