Have you looked at AAT Kings http://www.aatkings.com ? They were the first company that sprung to mind, but I'm sure there are others.

When we did a month long tour of the Far East and Australia we planned it with a local travel agent and all the flights were with Qantas. We didn't have a rep or a tour guide, btu we didn't need one.

I would also recommend visiting Cairns/Port Douglas as you can scuba dive on the Great Barrier Reef there.

Not sure if you can still climb Uluru, but it is not a gentle, easy climb. People we met on the way turned back.

Try to take in a show at the Opera House in Sydney as it is a great experience.

If you decide to DIY then theree are some great beaches on the east coast such as Byron Bay and Lennox Head. Surfers Paradise and the Gold Coast are very touristy. Brisbane is a great city.

luci

I have taken short tours in Australia with both AAT Kings and APT (Australian Pacific Tours) http://www.aptouring.com.au/ both were very good and both do a number of tours of various lengths. Both are Australian companies but I believe they may have UK agents.

We used Austravel for our flight and stopovers, but they do a selection of trips.
For flights in Oz, try Jetstar and see if you cn find the Friday Frenzy site for real discount flights (Still Jetstar). Virgin Blue also do good flights, and if you mix and match those two, you might do even better.