From Cunard Cruise Line:
On transatlantic voyages aboard Cunard Cruise Line's (cunard.com) "Queen Mary II," both cats and dogs are allowed to travel with their owners. An on-board kennel master is in charge of pets' regular feedings, walks, indoor playtime and clean-up. Upon arrival to the ship, pets receive complimentary goodie bags that include name tags, food dishes and toys. Pets are supplied with beds, blankets, gourmet food, snacks and either individual playtime or group playtime. Owners may visit pets throughout the day in two-hour blocks of time. Cunard recommends that passengers book their passage as far in advance as possible, as Cunard Cruise Line allows only 12 pets per voyage.
Not sure if they need to buy a ticket for them or how it all works. I've seen quite a few service dogs on Celebrity but haven't heard about normal dogs. Maybe it was a service dog but was being walked by someone else? Personally I wouldn't mind as long as they keep away from the main dining rooms, or have pet free zones for those passengers who don't like animals or are allergic etc.