In my honest opinion you should have a passport to travel with anyway. I don't think you need it for Barbados, they tried to do that earlier in the year but I think it was shot down. But for the ease of travel, in and out of airports it is highly reccomended. For the cost, it isn't that much and they are good for 10 years.
Barbados is the country that STARTED this whole Q. Check w/ the US state department & do not rely on what anyone else, including Carnival says. I think the current status is that tourists must have a passport to travel to Barbados but when the cruise lines howled, they amended it to say that transient visitors, like cruise passangers, who are staying less than 1 day do not need one.
A passport is the best form of ID you can get. Over it's 10 year life, the cost breaks down to less than $1 per month. There is no good reason not to get one. Since you have time, just do it. Better safe than sorry b/c if Barbados or any other country on your itinerary changes the rules right before you leave, then what are you going to do?