Actually believe it or not...
The "Admiral Stardancer" (which later became the "Viking Seranade") used to allow small dogs on board for those passengers that brought on their campers, trailers and/or motor homes. (The R.V. thing is even more amazing!)
As I remember, there was a small exercise area and your pet could be housed in your R.V. Of course passengers were allowed and encouraged to visit their pets.
This was a lovely ship. It was my second cruise some 25 years ago and David's first cruise. It was our first visit to the Mexican Riviera. Times have changed a bit since then.
P.S. Yes I would take "Knock-Knock" (our miniature dachshund) on a cruise should he be allowed,