I turned up a few tours that went North out of Perth up to Ningaloo Reef to Broom to the outback and then to Darwin. Darwin to Alice is then straight down the highway by Greyhound or an internal flight. Maybe that would suit you better?
That sounds epic, what are these tours like, is there plenty of young backpackers on them. Travelling on my own for most of it, so want to meet some cool people to hang out with.