Welcome to the forum!
First thing I'd do is use Google Maps to provide you with a route. I've done that bit for you (mostly, I don't know actual addresses so I've just picked a spot in each area).
Click here to see the Google Maps "fastest route".
Next I'd consider HOW you're going - you don't say if you're just sleeping in the cabin of the vehicle, swags on the ground, towing a big van, staying in hotels ... these do make a big difference to how you travel. You can't stay on the road until 10:30pm at night and expect every hotel owner to be happy to show you to your room, but towing a big van has a fuel penalty - actually one that I'm happy to pay for the greatly added convenience.
Take a look along that route, planning to stop for fuel every 400-500km (no towing) or 300-350km (towing) at the most in case you need to turn back or be diverted because of weather. It's a good - no, GREAT idea to have a couple of jerry cans in the back with some extra juice just in case, too.
I found that knowing there was fuel a certain distance ahead helped keep my mind at ease. We mostly refueled at large fuel stops, except for one (Kings Creek Station) and had no problems with fuel.
That out of the way the only other trick I can think of is to wake early, drive for a while, stop for breakfast and make sandwiches for lunch at this point, then drive right through lunch time and stop for dinner, then continue driving and start looking for a place to stop at about 10pm. At 10:30pm the roos get onto the roads and become a bother. That's for the middle of summer - I guess it's about 2 hours after sundown. Driving like this, you can maximise the distance covered each day - my wife and I managed 1,600km in a single day like that.
Was that the sort of tips you were after?
If you're looking at what spares to carry, I'd load a spare fan belt, all your radiator hoses, some rescue tape, duct tape, muffler bandage/putty, electrical tape, a variety of fuses, at least one spare headlight globe, one good torch per person plus a free-standing one that can be used as an area light, and most importantly 8 litres of water per person per day just for drinking purposes. Be aware that many, many places along the way won't have decent drinking water, so be prepared to stop in a supermarket and buy those 10 litre water bottles. Oh, insect repellant and a good surface spray to kill nasty bugs like spiders is also handy.
Oh, take a decent camera and shoot LOTS of pics, even while you're driving - have your passenger snap away at anything and everything. My wife did that while we were driving and now we have some fantastic memories of our journey.