Although they weren't 10 months old we brought our 4 and 7 year old children to Cayo and A.C We only planned activities or trips that we could do with them. We hired a babysitter through our hotel (Banyan Bay) for a snorkel trip, only because our 7 y.o. didn't want to go on another boat. The babysitter was great and our "date" was too. If you want more info I'm sure I could get her number for you.
Our pediatrician was extremely helpful in our planning. She sees a lot of kids who travel overseas so we trusted her advice on shots, whether or not to take antimalarial drugs and insect repellent.
We didn't really consider it an option to not take them to Belize. Now, they'd be furious if we ever went without them, darn it! We hope to enjoy some "grown up" vacations too someday and A.C. would be a great choice.