Hi there

Avoid filling up at small petrol stations, as often the fuel in these places is old and contaminated or stale. Stick to the big brand name ones on the highway which turn over a large volume. Particularly if you have a diesel with a particulate filter
Most boring section of road is from Port Augusta to the NT border.
Coober Pedy is a hole. There's a reason people live underground there - because above ground is a dump. If you have kids, don't let them wander - there's mine shafts everywhere. The breakaways are worth a look (where they filmed the original Mad Max movie).
Uluru is struggling financially since being given back to the traditional owners, so definitely stop in there. The sounds of silence dinner is definitely worth it.
Kings canyon rim walk is nice and the road is now sealed, but it's quite a long way off the highway to get there.
Consider driving along the West McDonnell ranges and walking day sections of the Larapinta trail. Multi day trips here require food drops and careful planning of water requirements.
Kununurra - joy flight over the bungle bungles if you can afford it (I'd avoid a piston engine plane and go in a turbine). Hidden Valley national park is right in town and despite being very small, is great to spend a day or two exploring off the track.
With a four wheel drive, the Gibb River Road offers a lot - but the road needs to be in good condition, as does your car. The road is littered with 4wd drive wrecks which have broken down and been abandoned there because it's too costly to tow them.
Go to the Bungle Bungles if you don't take the Gibb River Road. Not much at Halls Creek, likewise Fitzroy Crossing - although the Geikie Gorge tour is quite interesting.
Derby - don't bother, I lived there for two years - it's a dump.
Broome - nice, but very overrated. Accommodation very exy. Cable beach is nice, markets are interesting. Again depending on finances, a scenic flight or day tour via Cape Leveque and the Horizontal Waterfalls might be a nice way to end your trip.
I drove from Derby direct to Adelaide once with my uncle, stopping only for fuel. We did it in just over forty hours.