Remember that Australia is roughly the same size as continental USA and the "outback" (Gunbarrel Highway, CSR, Birdsville track etc) is in the middle. Its a long way to travel for 10 days without multi lane freeways, but it can be done.
There are excellent topographic maps prepared by various Government Departments, but Hema and Gregory's produce OK maps for route planning. They also produce weekend away books, trips that can be completed over a weekend within a few hours drive of the major cities. These cover the major 4WD areas around the cities.
Fraser Island is the Mecca for sand driving...a beach which has a posted speed limit of 80 kph, and inland tracks of 2nd low range. You can hire ex army Defenders fitted with knobbly skinny tyres. You can watch the tourists get bogged with amazing regularity
Southern NSW and into Victoria you have the High Country (Great Dividing Range). There are some excellent trips through there in both state forests and national parks with a wide range of driving terrain
Have a look at the Overlander 4WD magazine website as it does have maps and travel reports of different areas. Other magazines are Australian 4WD monthly and 4x4 Australia
Hire companies seem to like Toyotas, but I've never had to enquire about hiring one so I don't really know.
There's an awful lot of off roading available not far from any of the cities, so you should be able to find something to pass your time
Enjoy (and remember...we drive on the left)
Garth