Obviously a question of time. As Bevelman said, most on a time limit will hang a left at Townsville straight to Mt Isa.
If you can fit it in, the trip further North has much to recommend it. Certainly some better roads around the Atherton Tablelands and many interesting spots.
Winter good time to be up North, but note - the Tablelands will be cold!! (possibly also misty but if clear absolutely spectacular)
I have marked the roads mentioned on attached map (hopefully)
Quicker trip is take the Palmerston Highway at Innisfail to Millaa Millaa while the famous windy Gillies is accessed by going a bit further north to Gordonvale and turn left to Yungaburra.
I love this whole area but I am no fan of Cairns itself, best avoided in my opinion (I did live there for a while). However there is also a rather lovely coastal road (best done early morning) which runs North from Cairns to Mossman. (Again avoid overhyped tourist areas like Port Douglas

)
If you took a trip up there you could come back to the Tablelands inland via Mt Molloy and Mareeba.
Obviously we an keep making suggestions (and I'm only talking about a small area of Qld) but end of the day impossible to cover everything in the timeframe, so your work is cut out chopping out the bits you can't cover