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The only cruise line I am aware of that accepts pets is Cunard. The following can be found on the Cunard website:
"Queen Mary 2’s kennel programme is available on all crossings between New York and Southampton in either direction, and is overseen by a full-time Kennel Master who takes care of responsibilities such as feeding, walking and cleaning the ship’s 12 spacious kennels. Travelling dogs and cats also receive a complimentary gift pack and other animal amenities. The kennels and adjacent indoor and outdoor walking areas are open throughout the day, enabling guests to spend significant time with their pet. Reservations for the kennels may be made at time of booking, and are based on space availability...
It is very expensive to take your pet.