But hold on, the cruise is May 3rd.. I wouldn't send away for a passport now because they would need the birth certifcate. You probably won't get that back in time to go on the cruise and then you are stuck. Make sure she has a true certificate like the others have told you and you'll be fine for this cruise. If she likes it and thinks she will go on more, then go ahead and submit for the passport when you return.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013