I would check into some different cruises for both Carnival and Disney....You can most likely cruise with Carnival for almost half what a Disney cruise would be, which always seem to have great reviews. While the CArnival ships and kids programs are great, so are Royal Caribbean's.
YOu may want to go into the "first cruisers" section here and do some research:
Thanks I have read numerouos topics on the message boards here as well as the reviews, but still am a little lost on which one to pick. I probably will pick Carnival due to the lower prices, but which Carnival ship is the best when cruising to the Bahamas?
Note that the shorter Carmival cruises, such as to the Bahamas that you mentioned, tend to be more 20 and 30-somethings partying. While Carnival always has lots of families on board, it will be a different atmosphere than Disney's on the short cruises.