What about a train, or bus, from Adelaide to Melbourne ( about 12 hours ). If you can get a bus through the day you can see 700km of country between Melbourne and Adelaide, and there will be a few rest stops where you can get out and sniff the air and stretch your legs.
Then the Ghan from Adelaide to Darwin ( not sure exactly, but probably about 31/2 days ). Of course The Ghan is one of the world's great train adventures. The track from Alice Springs to Darwin was only just laid about twelve or fifteen years ago.
From Darwin, hire a car and make your way back towards Melbourne. There are many ways to choose to come back south, but the 'classic' tourist drive would be across from Darwin to Townsville, via Mount Isa, and then down the east coast through Brisbane and Sydney. A lot to see between Townsville and Melbourne. A beautiful drive! But the exact opposite of the first half the journey. Lots of towns and cities. Fast, new highways, with four lanes ( 2 each way ) for much of it ( Brisbane to Melbourne ).
You would need about 7 or 8 days from Darwin to Melbourne if all you did was drive from morning into the night, 12 or more hours every day, with just a few short rest stops each day. So if you took two weeks you can see that it is still a pretty quick driving holiday, but possible.
You could save a day by driving south from Mount Isa, through Longreach, Roma and direct to Brisbane. The road from Brisbane to Sydney, the Pacific Highway, follows the coast quite closely. And you get to see some more great 'outback' towns, and a lot of classic 'cattle country' through central Queensland. Some great landscapes through this part of the country from Mount Isa to Brisbane.
You would see five capitals - Melbourne, Adelaide, Darwin, Brisbane and Sydney. Also the iconic outback town, although briefly, of Alice Springs ( not sure how long the train stops there - hopefully for a couple of hours at least. ) And many great towns and sights in between.
This trip would let you see a big variation in landscapes and also types of towns, from the smallest outback towns, with just one or two buildings and a handfull of residents, to the two largest cities - Sydney and Melbourne. You will see the great wheat fields of the south, the deserts of the outback, the tropical greenery of the north coast of Queensland, and Australia's Great Dividing Range that runs right down the east coast, and even around the corner into the middle of Victoria.
Also July and August are great for touring through the top half of Australia, since it is the dry season. There are just too many cyclones and too much rain to risk going through from Darwin to Brisbane on a fairly tight schedule in the summer. Plus it will be a bit cooler for you.
So if you love driving, and covering a lot of km in a short time, as I do, you could actually see a lot of this big country in three weeks. You would definitely need three weeks minimum, or you will be driving while very tired in the last few days and it would not be safe or fun! If time was running short, you can drop the car off in Sydney, or before if you have to, and jump on a jet to get back to Melbourne quickly.
Good luck with your planning, and have a great holiday which ever way you go.