I have done Sydney - Darwin a few imes and been Darwin - Perth a few as well.
I would go from Sydney up through Mt Isa - Katherine - Broome.
If youbwant o do it in minimum time, I would allow 4 days driving daylight only.
The average car has plenty of range between fuel stops, I.e. around 300 kms max. Roads are fine during the dry, maybe a different matter during the wet.
I would stop around Charleville, mt isa, Katherine then Broome. Really long days but it can be done.
If you want to go the way you suggested, mil dura, cooper pedy, Alice, katherine, Broome. There are road houses in between the places I suggested that would allow you to do more kms a day.