Hi Amy,
Welcome to the Moms Panel! You've asked a really great question yet it's one that can be difficult to answer because the requirements have been continually changing over the past few years. At this time you do not need a passport to cruise from Port Canaveral to the Caribbean destinations. You can see a list of the acceptable identification
HERE.
Now to throw my two cents in...although at this time you are not
required to have a passport to sail to the Caribbean, I would go ahead an get it anyhow. Passports are required to enter the United States via air, so I always want to be prepared in the event of an emergency. Should someone in my party experience a medical emergency of some sort, I want the flexibility to fly back if necessary. If you do not have passports this will not be an option.
Additionally, with the continually changing requirements it would be better to prepare for it now, rather than to have to scramble at the last minute should things change.
I hope this helps, happy planning!