Derby is SO close to Broome that its not worth a night stop. (unless you REALLY like mudcrabs)
Take a swag with you - sit it in the boot of your car, and you just unroll it when you get to where you're going. Sets up in seconds, unlike a tent, and will be of use to you even in Broome, when you spend your first few weeks camping on some other pilot's floor. (Actually, stay at the Kimberley Klub.)
OK, How about this for a route:
Day 1: Brisbane to Roma. Roma is 475km away, and if this is your first long drive, you really won't want to go much further than that on your first day. Also, you won't be able to leave Brisbane as early as you plan to - you will be delayed, even if its just for one last cup of tea with the family.
Take it easy for the first couple of days, until you get used to the long driving.
Day 2: Roma to Longreach. Its about seven hours, almost exactly 700km, and if you get there in time, you can have a look at the Qantas museum. You can gradually build up the amount of driving you do in one day.
Day 3: Longreach to Barkly Roadhouse. This is almost 1100km, but on the western side of Longreach, you can easily sit on 110 the whole way, and by this stage, you'll be very used to driving. Fill up with as much fuel as your vehicle can carry in Mt Isa. The Barkly Roadhouse has good value hearty meals available, and you can camp for next to nothing. Dont forget to change your watch back 30 minutes as you enter the NT. This would be your longest drive in a day.
Day 4: Barkly Roadhouse to Katherine (Via Threeways). You save 100km by not going via the Barkly Tablelands, and the trip is about 850km. This will feel like a quicker day than the day before, which will give you time to stop at Mataranka, about an hour south of Katherine, for a swim in the hot springs.
Once at Katherine, have you considered visiting Darwin? There's a few companies there that put on green CPLs.. Darwin is just over 300 km from Katherine, so even if you do a day trip, up to YPDN, drop off your resume at a few places (Directair, Chartair, Hardys, Barrier, the usual), and head back to Katherine, you'll easily make that in one day.
Day 5: Katherine to Halls Creek. Its less than 900km, which gives you time to stop off at Kununurra to drop resumes off at Alligator and Slingair, and refuel for the rest of the drive. At Halls Creek, either unroll your swag INSIDE the grounds of the airport (PM me or any WA pilot for the gate code), (remembering to display your ASIC on the outside of your swag), or spring the cash for a room at the Kimberley Hotel. Halls Creek is not a place to sleep in the long grass.
Day 6: Halls Creek to Broome. Its about 680km if you go direct, or about 750km if you go via Derby to drop resumes.
Pre-book a room at the Kimberley Klub, but as soon as you get to Broome, head straight to Cable Beach and admire Australia's best beach.
Drop resumes at King Leos, Broome Aviation, and Broome Air Services. Also talk to Skydive Broome, (if you have 10 hours on a C182 or heavier), as everyone who works for them gets a job with the charter companies sooner or later. Avoid the other charter place there.
General Advice: Never ever pass a petrol station without filling up. When filling up, never put in E10 ethanol crap - your fuel economy will suffer for it. The only place that sells it on the other side of Longreach is Katherine, anyway.
The Chook Man at Daly Waters isnt as funny as people will tell you.
Take a LOT of museli bars and Golden Circle fruit juices. They can keep you sustained if you cant find a place to get dinner or breakfast.
When entering Broome, the police like to set up a speed trap between the first roundabout, and the town. This is likely to be the first time you encounter police since leaving Queensland, so keep to the speed limit once youve entered Broome.
Do not drive after sunset. Set off at sunrise (easy if you have a swag, because as soon as the sun hits it, youll wake up in the heat) and drive only til sunset. There are too many cows, water buffalo, and other animals out there. DO NOT DRIVE AFTER SUNSET.