Yep do it easy . Take your time . Nice cattle station stays up there . I tend to break the distance in quarters . Using or writing in maps 8 or whatever # it is up to now . To try to get rough travel program . Just be aware of national parks . You not âsupposedâ to camp in them overnight .

Given the lateness of the current wet season up north, I do not think you are leaving your trip north too late.
It will be the mid June-end July school holiday period (roughly) that will be the busiest across the top part of WA and NT.
My main concern would be that, by late August, it is getting rather hot and dry in the Kimberley and Kakadu and the like.
I do not understand Aus-Kiwi's reference to not camping overnight in National Parks?? You are supposed to use the online booking system for many of them, now, but I do not believe there is an issue with staying one night only.
If you are planning on visiting National Parks in WA to any great extent, might be worthwhile buying an annual Parks Pass.
Depending on when you look like getting there - which you will have a better idea about once you are on the road - might be an idea, a few weeks ahead, to book into Broome - it could be getting pretty busy after about mid June.

As Aus Kiwi has already said, just take your time

I done that trip from south of Perth to Darwin in July, August, September last year (2017), it was hot in the Darwin area

We stopped a few times on the coast in National Pk area. Twice and lucky it wasnât the same ranger . We where asked to move on . NO overnight camping . Or $300 fine . But then went on and told us the hours they work . We are completely dry set up . Black, grey water etc . Itâs the back packers that donât do the right thing . Not using toilets etc . One time there was a hell thunder storm . You would be crazy to drive in that . Lucky the ranger agreed .