Hey Sicilianmama,
It's possible, certainly.
From TWB to CNS, you can do in 2 days if you need to. From CNS, you can get to Bamaga in a day up the PDR (again, if you REALLY want to - I think Barrabart holds the record for that drive). Of course, that's driving 12-14hrs a day.
SO - back to your time scale. I think it's rushed, but I think it's achieveable. 3 days transit from TWB to CNS is a good idea. So long as you have kids that can cope with 3 x ~8hr stints. It's a good compromise between the flat-out 2 day run, and having to set up the camper 2 dozen times just to get here. If you want a bit more comfort on the way up (if your finances allow it), it's lovely to be able to roll into a motel at the end of a long day on the road and not worry about having to set anything up. I've never had any trouble at all getting motel/caravan park cabin accomodation in Mackay/Gladstone/Rocky with no prior booking.
Which leaves your 8 days for the cape. The PDR is a dirt highway, built to go from Cairns to the cape (and Weipa). You've got to be careful with speeds on it, and it's usually corrugated to hell, but it's basically a decent condition dirt road for the semi's. No worries with taking a stock 4WD + camper - for that matter, no worries taking a stock sedan and caravan either.
If you wanted a bit more adventure, what you CAN do is head up the OTT, and just take the bypass roads around anythign resembling fun. Most of the creeks and gnarley bits you can bypass by popping back onto the PDR, and then pop back onto the OTT further up. Friends of ours did this a couple of years ago with a bone stock 4WD - they still got to see all the famous places, just had to backtrack to go back to the bypass roads.
If you counted on 5 days for that drive up to Bamaga, one day in Bamaga, then two days back to CNS via the PDR, I wouldn't think that would be terrible. It'll be quick, sure, and you'll miss an awful lot. BUT, for a first big trip, towing a big, wide camper, with kids in tow, you could do a lot worse.
Or put it this way - my theory is you're better off doing it and having the experience, than sitting at home sulking that you don't have 4 months off, so can't even contemplate it. Go up, find the spots you like, and come back later for a more targetted holiday if there's certain spots you fall in love with.
Question - taking another car with you? Or just you guys?
Good luck - it's an adventure!
Matto