Why not form a 'team' and enter the RFDS Outback Air Race? There should be one coming up soon. You can get sponsors to help cover the cost of the plane, and then work on donations for the RFDS.
We did it in 1998 from Alice Springs to Broome via Darwin (and obviously had to go Perth - Alice Springs to get the plane there) and it was a wonderful experience, with the added safety of having 30 light planes nearby for the remote bits.
We did Perth - Sydney - Melbourne - Adelaide - Perth the year before, and as long as you be mindful of the weather and don't go with the 'must get there because accom is booked' philosophy that nearly overwhelmed us, you'll have a blast - wherever you go.
Horizontal waterfalls near Derby WA is magic as well as Jabiru & Bungle Bungles as previously mentioned.
Enjoy! I'm jealous...
Matt