AUSTRALIA - Car Rental

Hi BillP, car leasing in Australia is usually a longer term thing but car rental is generally easy with lots of the usual global as well as local car rental groups in most major centres. Depending on your wish list of places to visit travel distances might be rather long and flying may be a better option. Obviously you wouldn’t want you drive immediately after a long haul flight and a car can be a nuisance in bigger cities such as Sydney and Melbourne but public transport in the those cities is generally pretty good. It would be easier to offer suggestions once you have a more detailed idea of your travel plans.

Per Helen, distances in Australia can be vast, and having a vehicle in any of the cities will be more of a hassle than it's worth. Flying between major cities is much preferred. The Qantas low-cost carrier Jetstar makes it easy and relatively cheap to get around.
For exploring the countryside within a relatively small area (by Aussie standards) having a car is the way to go. The Blue Mountains and the Hunter Valley near Sydney, or the Great Ocean Road and vicinity near Melbourne are some that spring immediately to mind.
Renting a car is as straightforward there as it is in the US or Europe with most of the usual companies you're already familiar with represented. We've had good luck with AutoEurope.
Might add that Helen's home town of Adelaide is an under-appreciated little gem of a city. Do try to work it into your itinerary if possible.