To my knowledge only QEII has a kennel and no, you can't walk the dog. They have wire enclosed runs and they can go there for exercise. You can visit all you want but the dog stays in the encloser. It's much safer that way.
I traveled to Europe with my two cats on a Cunarder once. I was moving to Madrid for a few years. There were dogs onboard as well. It was quite rough. The cats loved it, hanging upside down from the kennel run wires. The poor dogs however were sick as well, dogs. I'd think twice about traveling with your dog. They aren't good sailors.
I know how you feel. The only thing I dislike about cruising is having to leave "Kramer", my Yellow Lab with family. I would love to take him on a cruise. If he saw the Buffet he would think he had died and gone to Doggy heaven.
But actually a ship is no place for a dog. Other than the QEII I know of no other ship that has any facilities for animals.
And truthfully a number of dogs and cats on ship would soon turn into bedlam and I think it would make the cruise experience much less enjoyable for others. My daughter is a vet and believe me when you get a bunch of dogs together at the clinic it can be a "trying time" for both the dogs and the clients.
Companion animals are another story. They can have accomodations made for them. I have read posts from an amazing woman and her companion animal who cruise quite often.
Pamda: Our First Time Cruisers editor is very familiar with this couple and their cruises.
I know it's hard to leave a friend but the look on their faces when you come back makes you feel much better.
I don't know everything about this but I do know a little bit.
Please don't take all this to the bank because I am not, by any means, the ultimate authority.
My understanding is that dogs (and, I would assume, possibly incorrectly, cats) coming into the UK or a colony must stay on board or submit to a six-month quarantine when coming ashore. That's more painful than staying at home in a kennel of with friends/family for a while.
So far as I know, the only pets permitted on cruise ships (QEII excluded) are companion or "helping" dogs. There are two kinds ... "eye" dogs and "ear" dogs. And, really, they are not pets.
The drill to get the helping critters on ships -- and offshore in ports
-- is quite stringent including vet visits within a time certain, possibly some innoculations, and lots and lots and lots of paperwork.
And I have to agree with Mike. Bunny and her companion, Erin, are totally remarkable.
Heck, Erin (dog) can find the cabin immediately. It usually takes me three or four days.