We've just got back from Cape Range. It is very difficult to get a site at any of the camping areas north of Yardie Creek. There is always a long queue at the gate in the morning and only a few sites available each day. The best thing to do is book one or two nights at any the sites were you can book on the Internet through DEC. once you arrive tell the camp host you want to stay extra nights. The next morning all the camp hosts get on the radio and work out how many sites are available and how many people want extra nights. At least when we were there most people that wanted extra nights got them, although you may have to move to another camp. Once the hosts have sorted out who wants to stay extra nights any spare sites go to people queued at the gate, hence why there's so few sites available to people who line up.
Re sites. We stayed at Karajong camp. Big sites and well spaced out, but no shade. Other camps had some shade, but campers were squeezed in more tightly. Best thing about Karajong is there is a small coral reef right on the shore which is great for kids. I could even wade out about waist deep and hold our toddler so he could see the coral and fish.
Good luck getting a spot, it's a great place.