If you really want to see the Kimberley in the wet fly up into Broome for a couple of days, have a look around then fly back down south, you can score some very cheap flights and accommodation at that time of the year. It's a far more efficient use of your time and $$$. You can drive all the way through to Broome from Perth in as little as a day and a half with two experienced country drivers but you are still talking 2200km.
I worked with a couple that could do Perth to Halls Creek in 30 hours (3000 km) but that is a serious undertaking

If you only have three weeks keep your road trip to the south west at that time of the year, probably no further north than around Geraldton. Any further north and it will probably be too stinking hot and chew up too much time.