Dangerous marine stingers are usually found around mainland coastal beaches, and Lizard Island is some 30km from coast. So, its unlikely you'll encounter them there, but check with staff on day, there's a research station on Lizard Island so they'd be up to date with any relevant info. If you're worried, just rent lycra stinger suits, they'll also keep you protected from sun which can be pretty strong in November.

Look at this website www.daintreewild.com.au and as you have a large family I am sure that everyone would love to spend time with the animals which roam around the little zoo there and you can feed the animals as well. The accommodation is nice as well, as is the swimming pool right outside the rooms. I have stayed at this place and thought that its is absolutely not to be missed by tourists.

Also look at the Australian government site on tour to the Great Barrier Reef. They provide reputable tour operators and different places to experience the reef:
http://www.gbrmpa.gov.au/visit-the-r...rism-operation

By all means, if your finances allow, go to Lady Eliot Island! Its an all-inclusive trip... LOTS of snorkeling, and it can be enjoyed by those who have never done anything like it. For the little more advanced, you can snorkel out to the "shark hole" and see reef sharks daily. You can also snorkel out and hover over a sunken ship. Its an amazing, once in a life-time experience. They have 3-night packages (or more) and day-only packages.