Oz Interior trip
I organised a trip for 5 couples in 2004 flying C172 thro' Goana from Brisbane. Unfortunately they went out of business thro' Government rules of ID cards which can only be acquired in OZ after waiting 7 days. So do check this out if still relevant.
I believe you can self-hire from Perth and there is a company called air safaris international who are not cheap, but organise groups which ensures safety. It is a big country with large expanses of desert and esy to get lost.
However its a good idea and well worth exploring - do not miss Coba pedy and Alice Springs.