Hi Frank956,
First off, as an Aussie I can tell you that Fraser Island & the Whitsundays are not mandatory - if I had to nominate some of the "must sees" they'd be the Rock, the Daintree and the Great Barrier Reef (GBR). Then add to that Kakadu, Litchfield, Katherine Gorge, the Kimberley and the Bungle Bungle.
Basically, May through to October - see the top half of Australia and November to April the southern half. Anything south of say Rockhampton the water will be too cold for swimming. And on the west coast, north from Ningaloo Reef/Exmouth is warmer.
What is your budget, will you be staying in hostels, doing tours, or taking transport? Will you be hiring a vehicle, do you prefer to see cities or natural attractions or a combination of both?
You have the choice of travelling the top half, Cairns>Port Douglas>Cape Tribulation (you could continue further north to Cooktown), then fly Cairns to Alice Springs>Ayers Rock/Uluru, then Darwin>Litchfield>Kakadu?Arnhem Land>Katherine then over to Kununurra and down the west coast to Broome and the Kimberley.
You have the time to do a half circumnavigation - Cairns>the East coast>Sydney>Melbourne. The GOR>Adelaide, then up the centre Ayers Rock/Uluru>Alice Springs > Darwin.
Depending on which city you'll be flying out of, should you choose the latter, I'd recommend you do the east coast straight away before the temperatures drop too much.
Also in the Top End, the Tiwi Islands and Arnhem Land are IMO also "must sees".
Our budget airlines are Virgin Blue...Jetstar, and Tiger Airways. currently, Jetstar have what is known as "Friday Frenzy" - between 4.00pm and 8.00pm AEST, cheap flights and specials are available. They vary from week to week and the downside is are only available for travel during certain dates.
Greyhound is our interstate busline - see route map;
and Firefly buses travel Sydney>Melbourne>Adelaide. Great Southern Railways (GSR) have three trains - see map route. As an international traveller you can purchase Rail Explorer Pass which is currently AUD$590 and is valid for six months from the first date of travel. You can effectively travel from the east to west coast, down to Melbourne and up the centre to Alice Springs and Darwin. The pass entitles you to a day/nighter seat.
Personally, I would suggest a combination of flying and bus. I've travelled on all three trains - Gold Kangaroo (First Class) on both the Ghan and the Overland (the Overland was until recently an overnight service to Adelaide) and greatly enjoyed it. I went tourist class ie a day/nighter seat Perth to Kalgoorlie and they were the most uncomfortable seats I've ever sat in.
I'm happy to post up information so let me know which places you're interested in.
Cheers.
[ Edit: Edited on 14-Mar-2009, at 19:50 by Whistler 2 ]