Can't help you with Melb - Ayers Rock. or really Melb to Perth.
However I have driven from Sydney to Perth and it took us three days of solid driving to get there.
Along the way we stopped to check out the Barossa Valley, and a few little other towns, but our main focus was on getting to Perth.
I have to say that driving across the Nullabor Plain is the most boring bit of road I have ever been on and once we arrived at Perth we thought of any other way we could get back so we wouldn't have to do it again
Phoebe