If you insist on taking your pet along, the Cunard Queen Mary 2 can accommodate some pets, but many restrictions apply. For example, the pet has to stay in the onboard kennel area (not your cabin), and the cruise fare is not cheap.
One other thing. As much as your dog or cat loves being with you, they probably do not like strange environments. Can you imagine how stressful cruise travel might be for a pet who doesn't understand it is supposed to be fun?
Can I Take a Pet on My Cruise Vacation?
What do you think about cruising with your pet? Take our cruises poll, and/or add a comment below.
Cruises Poll: Would you like to take your pet on a cruise?

