Leisurely drive from CNS to BNE??? It's about 1700km's and with three kids that's even longer! I know I've done the trip heaps of times as I used to live in North Queensalnd.
Some of the coast is great but the road generally is terrible single lane. If you want to see the State great - but just give yourselves plenty of time if you chose this option - and make sure you stop in at Airlie Beah and the Whitsundays (Island Group)