Don't try to do too much!! Darwin to Melbourne is like travelling from Oslo to Cairo! I would agree that Perth is a nice place and rotnest island is beautiful but they alone probably don't justify the long trip to the west coast. If Sydney is part of your itinery, take in the Blue Mountains and go to the aquarium in darling harbour.
Melbourne is a great contrast to Sydney with it's old trams and European feel. Beautiful botanical gardens and you could take a few days driving the great ocean road in Victoria, and see the twelve apostles.
However for me, if I was in Mebourne I would definitely go to Tasmania. In fact you could spend the entire holiday there. A 50 minute flight from Melbourne or take the ferry (The spirit of Tasmania) for the 14 hour journey. I would recommend the former.
Fly into Hobart and enjoy the feel of the small city at the foot of the beautiful Mount Nelson and Mount Wellington, with the beautiful Tasman Bridge over the Derwent River. Or eat fresh seafood on the wharf at constitution dock. They also have a wonderful market at the beautiful Salamanca Place.
If you go to Tassie, you must go to Pot Arthur on the south east coast and Strahan on the west coast and do the World Heritage Cruises tour down the beautiful Gordan River.
They also have one of the top 10 beaches in the world, Wineglass Bay on the fraycitet peninsula near Coles Bay. To get there, there is a great hike for the kids over the pink granite Hazard mountains. Stay in the Fraycinet Lodge. If you are into hiking and nice lodges you could also check out the Cradle Mountain Lodge.
Tassie has it all, beaches, mountains, small towns, city life, and great wine, especially if you like Pinot Noir. The place is about the size of the republic and has a 1/3 of the population of Dublin.
I've been all over Australia and Tassie is the place I miss most.
For me I would do Sydney, Melbourne, and Tasmania. Cradle Mountain Lodge, Fraycinet Lodge, Hobart, Strahan, Port Arthur (that's just a day trip from Hobart) and possibly Launceston. They have a beautiful gorge that runs through the city!
Sorry to be so long winded but hopefully it's of some help. Google some of these things and let me know what you decide.
Patrick