Uhmmm I guess we do have a desert lol. We call it outback Australia, which is basically the centre of the Australian continent. Our continent's very dry and arid. People do live there though, there's a city called Alice Springs in the middle of Australia, though mostly it's inhabited by Indigenous Aboriginal Australians.
I've never actually been to the outback; I was born in the city and everything. The majority of Australians live in the cities (Sydney being the most densely populated). If you want to visit the outback though, make sure you pay a visit to
Uluru. It's quite a popular tourist attraction. I've never seen it before but I'd like to one day. =]