We went on the Disney Wonder during Spring Break; our kids just absolutely loved it (maybe as much as Disney World itself).
At the time they were 3 and 7 and both found plenty to do. I can't remember if they actually have babysitting in the cabin, but the kid centers make it completely unnecessary.
I have to say that neither of our kids our, in any way, shy, but even our friends children (who are a bit shy) still enjoyed it.