The only houses in Australia that are underground in any way are those which are 'cut in' on a steep slope but I wouldn't call that a basement, or maybe the people who live in caves...but they're not really basements either.
The only people I can think of who have basement like structures in their houses are people with wine cellars, but even they are few and far between in these days of air conditioning.
There'd be more in Sydney I suspect, but I don't know of anyone in Qld with a basement. We like living above ground up here.
