"And don't go too far off the beaten track and get yrself lost. Getting lost out that way can be really dangerous". Very dangerous. As you know, Oz is about the same size geographically as the US. Big difference is population size. We've got 23 million. The US has 320 million. And most Aussies live on the coast. That means lots of "off the beaten track" places are empty. If you really want to get off the beaten track, consider taking an organised tour. Sounds boring I know but you'll be lead by people who know what they're doing (hopefully) and have the equipment to get out of a sticky situation. As way of illustration, here's some Aussie humour...
In Australia, we have roads on which you won't see another car for hours or even days. If you're going to be travelling on these roads, take a blanket and a pack of cards. If you break down, find a shady tree, spread the blanket and sit down and start playing patience. Within five minutes, you'll have someone looking over your shoulder saying "That's not how you play patience."
More seriously, consider other possibilities than driving all that way. My suggestion? Hire a car in Adelaide and explore the Flinders Ranges, Kangaroo Island, the Adelaide Hills and the Victor Harbor area. Then fly to the Alice and hire another car and go to Uluru and the Olgas. There's some pretty interesting gorges to the east - much overlooked by tourists. Then fly to Darwin and hire another car! Have a look at Kakadu and Litchfield. Watch out for crocodiles. No, I'm serious. You can go swimming in a croc cage in the city centre, but apart from that any other body of water is suspect.
Other tips...ask the locals as Violet has said. As soon as they hear your accent, they'll fall over backwards to help you.
Use Google to look at temperature etc in all three places. August/September is the cool part of the year and if you're camping out, it can be quite cold in the bush. Darwin is always hot. It has basically two seasons, the Wet and the Dry. And maybe the build-up to the wet, known as Mango Madness or the Suicide Season. But you'll be travelling during the Dry. But it will still be hot in the Top End.
Take water with you. Lots of it, particularly if you go hiking.
Try a Violet Crumble. And Tim Tams. And Chocolate Mint Slices. And Monte Carlos. Try vegemite once just to convince your self how awful it is.
Drive on the left. If you've never done it before, it's pretty terrifying at first. I'm an Aussie living in Holland and have been back to Oz on many occasions and even I have to think about the switch.
Hope this info is helpful.
Edited to add...
You can take a train from Adelaide to Darwin. It's called The Ghan. A sit-upseat will cost around $900 (Oz) and you'll get to see a lot of the country. You can get off in the Alice and reboard a day or four later.
Go to an Australian Rules Football game. The mighty Port Adelaide and the despicable Adelaide Crows both play at Adelaide Oval which a short walk from the city centre. I support one of those teams, but in order to not sway you one way or the other, I won't say which.
A word about bringing in foodstuffs...our Customs are friendly, fair but FIRM. They generally take a dim view of people bringing in foodstuffs. And not just foodstuffs, any product made from (say) wood. When I brought my guitar in, they checked it out even though I had actually bought in Australia. If you try sneaking it in, expect to spend quite some time talking with the men and women in blue and you'll leave with a bit of a hole in your wallet or credit card.
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