I took three weeks to do the Gibb River Rd from Tom Price, and that was just the main road itself, no detours, and no more than 2 nights in any spot (except a couple extra in Broome and Kununurra. Add an extra two days either way from Perth, and you are close to four weeks.
If you've already done the coast around Coral Bay and Exmouth then consider going inland - from Perth you can do a really nice three week trip to the Pilbara without rushing and seeing lots of good stuff. Millstream National Park, Karijini NP, Tom Price, Newman, Marble Bar plus I hear that Kennedy Range and Mt Augustus are well worth visiting.
You can always break up the trip with a few days at the coast of course!
That time of year is good in the Pilbara, not too hot, plus many of the water holes will still have water in them from the summer but it doesn't get the monsoonal rains and flooding like the Kimberley.