Cunard also sounded like a great option (we were going to relocate the other way) a number of years ago, but they were also fully booked during the times we needed too. Sadly, your dog is not allowed in your stateroom, but must be kept at the kennel area for the entire duration of the trip.
If you do find someone to share your charter, please report back on how the charter went and which company you decided on. We are always interested in hearing about traveling with pets