Best place to post this suggestion would be:
Overlander 4WD :: Index
both these forums are well visited by australian 4wd enthusiasts
The best time to travel in Australia is during the European Summer, June - August, as the outback can reach 45-50˚C in November - February, not the right time to do anything bar the east and south coast…
Also, most Australian's wouldn't want to be touring Europe in winter time!
If you're planning on doing 3 months, you might want to consider buying a vehicle, and selling it again after 3 months. You can rent a roof tent, but get a vehicle (say, 100 series, or troop carrier), that would do the trick.
You can look at carsales.com.au and drive.com.au to give you an idea of prices… have a look around, there are often ex-brit rental troop carrier based campers for sale for around $20K.
This is of course if you get no bites on a vehicle swap!
best of luck