As
Globaliser says, there are only a few flights direct to Ayers Rock - we couldn't get in so flew to Alice Springs and took the bus. It's about 7 hours each way by road and an awful lot of very red desert to look at, but we found it quite enjoyable.
Rather than Cairns, I'd look at Port Douglas, which is a bit further North. It's nearer the Daintree rain forest, you can hire a car and drive up to Cape Trib(ulation - voted one of the top 3 beaches in the world) and there's the
Quicksilver cruises to the Barrier Reef (as used by Bill Clinton, if you consider that a recommendation!).
If you're flying Qantas, you may be able to get a better deal on the internal flights if booked together, worth investigating.