Unless you are flying to Ayres rock then forget it. Driving will take 3-4 days total – Cairns-Ayres Rock. Some roads N to S but forget E – W through the middle.
If you try the Ghan then invest a in sleeper (Gold). Katherine is a great stop-off if departing from Darwin
Avoid driving at night if in the outback – as Wombats and Roos etc can cause damage.
MCG for Aussie Rules is quite a spectacle
The Whitsundays have the best access to the GBReef.