From the Carnival site (which I'm sure you've read):
Is Camp Carnival Available for Children Under 2?
Camp Carnival is unable to accept children Under 2 years during activity times but we do offer babysitting services for you within Camp Carnival. Babysitting services for Under 2's are available each evening from 10pm-3am as well as our Family Play Times on Sea Days and during freeplay times on port days. All babysitting services for Under 2's are charged at babysitting price ($6.00 an hour). During Family Play Times on Sea Days parents with Under 2's are welcome to stay with their under 2's at no charge.
like you'd have to wait until 10 PM for the babysitting service. I think that Carnival will probably seat you with other parents and children, so maybe a "huge mess" won't be a problem
I agree with Luanne (no surprise there!) that you should call Carnival for a definate answer.