First excellent time of year to travel in the northern and central part of the country.
From Broome I'd suggest finding one of the stations (=very large farms, usually measured to the nearest quarter of a million acres) that offer farm stays in the Kimberley.
Some include
Mt hart
Mornington
Mt Elizabeth
Drysdale river
Home valley
El questro (this is arguably the most well set up for the tourist with lots of variety in accomm and on ground tours)
Kununurra is at the east Kimberley and the logical spot for fuel. I think drysdale has jet a1 too if req, but it would be $$$$. None except Kununurra are sealed either.
From Kununurra it's direct to ayers rock over a very empty desert but it beautiful in its own way, and worth a look at the Bungle Bungles (scenic flight pattern check Jepps, you might also contact ground tour companies who have camps there if you want a look around on the ground which is pretty spectacular) and Wolfe Creek Meteorite Crater. If aboriginal art is your thing, a stop at Balgo could be arranged with the arts centre, just a short walk from the strip (weekdays only, no accomm). Halls Creek is a bit north of Balgo and should have Jet A1, but I wouldn't recommend staying there
From Ayers Rock, you might consider Alice Springs for a day or two which has a bit to see as well - lots of gorges and desert scenery.
For something completely different and the quintessential outback pub experience stop at William Creek near lake Eyre. Accomm is basic around$110 a night in a very basic and spartan room, but clean. Make sure you are up at sunrise for the desert bird life. Ring ahead too as there are local procedures. Jet a1 by the drum but u shouldn't need it with your range.
From there, Broken Hill for jet A1 and on to Sydney.