We did the "Hot Spot Shuttle", which you take care of right inside the terminal. It's $15 a person (I'm not sure if it's the same for kids) and you get a wristband thats good for rides throughout the day. You'll get a map of places the shuttle stops, and Doctors Cave was the last stop. I don't think it's an excursion offered by Carnival (I didn't even check the Jamaica excursions they offered), and I don't remember seeing anyone standing in the terminal going there specifically, I had researched things to do in MoBay online on my own and had found that and we just decided to go there.
If you do this, you might want to ask where the shuttle stops first, and if you have to get off. The first stop our shuttle made was at the Old Fort Craft Market, which was the one place we wanted to avoid in MoBay. The people there selling their stuff are really aggressive, and we just aren't into that so we had planned on staying away from there. And we had to get off the shuttle there. Or, find out how much a taxi would be. I want to say you can get one for $4 per person to Doctors Cave (I thought I read that somewhere) and that would be a way to avoid the extra stops.
Yes, Doctors Cave Beach is acceptable for kids. There were several kids there, and since there are lifeguards there I think its a really safe place for kids. When we were there, a small 2 year old boy was wandering down the beach and he didn't get far at all before they caught him and started looking for his parents. There was a water trampoline out in the water too, fun for kids and adults lol! Plus, "they" say the waters of Doctors Cave are healing so we all jumped in. :)
November 2008-Carnival Valor (Miami, FL...Nassau, Bahamas...St. Thomas, USVI...St. Maarten, NA)
February 2009-Carnival Conquest (Galveston, TX...Montego Bay, Jamaica...Grand Cayman, Cayman Islands...Cozumel, Mexico)
August 2010-Carnival Dream!!!!