Agree with all the above, suggest watching the movie Wolf Creek, that should put the scare in ya!
As mentioned above take a fuel jerry with you, at least a 20L one, fill it in Sydney and make sure you leave it for an Emergency, don't plan to use it IMHO. Plenty of places to fill up along the way, but keep an eye out for "Last Fuel for XXXKms" signs, they can be extremely helpful. When it comes to fuel prices you'll be tempted to hold out till the next town because the current one seems way too expensive, this is fine, but make you chuck at least 10L or so at the expensive one just to make sure.
If you're happy to camp out in the back there are lots of free camping sites along the way, my old man does a lot of that sort of thing with his Campervan, he swears by an App called WikiCamps, it's like the TripAdvisor of the camping world:
WikiCamps Australia | Camping app for Australia | Travel | iPhone iPad iPod Android Phone Tablet | Camping, Caravan Parks, Backpacker Hostels, Day Stops, Rest Areas, Information Centres, Points of Interest, POI, Dump Points
I've done the trip from Brisbane a few times, Charleville is good to stop in, have also stopped in Blackall before, of course Mt Isa and Longreach are great stops. Three Ways has some nice cheap accommodation on your way and if you stop there you'll be able to strike out and make Kununurra in a day if you don't mind pushing it a bit, otherwise just stay in Katherine for a night then it'll be a breeze. You'll likely see reference to the "Buchanan Highway" which goes through Top Springs and Victoria River Downs and saves you going up through Katherine, THIS IS A TRAP, DO NOT USE IT!! I did it once, it's doable, but wouldn't recommend without being real comfortable with actual 4x4 driving. Personally I'd book in a room at the Barkley Homestead, stay there the night, drive from there to Katherine and stay the night then head to Kununurra from there. I have done the trip from Barkley to Kununurra in a single day but it's a bloody long day and I did it with someone else.
Oh, when you get to the WA Border there is a Border Station there and they check for Fruit and things like that, you can look it up and make sure you're not carrying anything. If you are you won't really get in trouble so long as you declare it but you will have to get rid of it.
You'll come across Road Trains which might be a new experience for you, be extremely careful when it comes to overtaking, if you can snag yourself a cheap UHF CB Radio this can be useful out that way for all sorts of things including over taking. Generally if you get in behind the Road Train so that they can see you with theor mirrors they'll give you a signal when it's clear, they'll just flick their indicators on so they flash a few times to let you know the way ahead is clear but don't take this as the be all and end all, use your own common sense, remember they're long and if you're in a 4x4 you might not have the acceleration, don't be afraid to use the brakes and slot back in behind him if something comes the other way, lots of people have lost their lives trying to push it. There are also now some Unrestricted Speed sections, which means no speed limit, you'll just see a sign with a black circle with a slash inside, feel free to make up some time there but once again, just like in Aviation, Personal Limits, if it doesn't feel right slow down.
Oh and bloody campervans, they're slow, they can't help it but they can make a nuisance of themselves going 80km/hr in a 130km/hr zone, they don't always have great vision if they're new at it or just not thinking so treat them with the same caution you would a road train when it comes to overtaking.
Also I'm with the others that said don't travel at Dusk, or night in general, it's just not worth the nerves because of the Animals. Emus are fairly rare in my experience and won't bother you too much, Camels you might see from time to time and are slow to get moving but will try to move out of your way generally, Kangaroos are the dumbest animals alive and have a tendency to match course with you and then try to jump across your path, no idea why, something to do with a lack of depth perception I've been told. Kites are a type of bird you'll see as you head further north, dirty brown ragged looking things, they are dumb as well, what they'll do is fly straight ahead of you and then at the last second they'll swerve side to side then pull up and over the vehicle, usually works, sometimes they time it wrong and you'll wear it on the windscreen so watch out for them.
Last time I was in Kununurra the booze is very expensive, grab a couple of Cartons in Katherine on your way, hide them in the back under a blanket so no one seems them (One thing certain people will almost certainly break into your vehicle for in Kunners) and take them with you, it'll make you extremely popular amongst the Backpackers and the new work colleagues too.
OH and last but certainly not least, have fun, have done the trip a couple of times, take your time, enjoy it, talk to people along the way, you'll have a blast, just keep safe and take precautions.