Hi Grant,
This is actually freaking me out a bit. My brother's name is Grant, and his wife is Sam, and they've got 3 little ones, about the same age as your 2. Why is it funny? Well, we all went to Moreton at Christmas time last year...
Here's the link to our trip: http://myswag.org/forum/index.php?topic=4951.0 - but it sounds like you've already probably seen it.
We stayed at the Blue Lagoon campsite, and I'd highly recommend it. It's actually quite a big site, and the amenities block was quite good. We camped down near the walkway through to the lagoon, and it was really very handy. If I was going to go back, I'd go to the same place. To be honest we didn't spend much time in the beach, but swum in the lagoon at least twice a day - it was excellent. Very safe for kidlets there as well.
You don't want to go to North Point campground - it's very open (IE, you can see EVERYONE else!), and the actual sites are fenced off from the road, so there's no way you'd get a camper onto any of the sites. I'm not sure if the DERM site mentions that now - it certainly didn't when we went.
Comboyuro Point is on the western side of the island, up near Bulwer. When we were there, the area around Bulwer was always very busy. On the upside, you're nice and close to the shop, etc. I'd be concerned about midgies/mozzies/sandflies on the western side of the island though - over on the east you get the sea breeze, and it seems to keep them away. The Rocks had quite bad mozzies when we were there - everyone had mozzie nets and midge-proof gazebos up. Also, while we were there, there were a LOT of sealice in the water on the western side, both up at Bulwer, and down near The Rocks where the barge arrives. I've no idea if that was normal though, having only ever been there the once.
All that said, we didn't actually stay there, so I can't comment on the campground itself. It is a bit away from Bulwer, which is nice, but still close enough that everything's handy. The ambulance & helipad are at Bulwer, so if you're accident-prone like me, that's probably a good thing!!!
All in all, we had a blast, and the kids really enjoyed themselves. The island is excellent to explore, we could have done with a couple more days, and we had pretty packed days as it was.
Good luck - it's a great place to visit, and I'm sure you'll have an awesome time!
Thanks!
Matto