Pick the Spring or Fall as a compromise

Other than Ululu, which involves detailed planning, other parts of Australia are very easy to reach - domestic flights are very frequent and reasonable. You can take bus which saves you 50% of the cost but also wastes valuable time - A trade-off you need to weigh it yourself.

Forget about the west side (Perth) and concentrate your trip on the Coastal of East side, Melbourne, Sydney, Bri*****ane (Gold Coast/Sunshine Coast), and Great Barrier Reef - that, imo, are your musts. Then you see how you can work the Ululu into the picture.

BTW, this route already covers 3 major provinces - Victoria, New South Wales, and Queensland.