I am a travel agent, and I have never heard this question before (first time for everything!)
I'm almost positive that you will not find a passenger cruise line that will accept an animal of any kind on board, but you might try looking at some of the barge cruises that defy many mainstream rules...
I think the largest obstacle you might face is that there really isn't anywhere on a sailing vessel for your pet to "do his/her outdoor business" and that is a health concern.
Not to mention each countries quarantine requirements.
Best bet would be to board your canine companion at a well respected facility close to your home, or anticipated port of embarkation.
