Fluffy is an abandoned character, only appearing in the episode "The Honeymoon". She was the pet cat of the Brady girls.
In "The Honeymoon", Fluffy was chased around the wedding by the Brady boys' pet dog, Tiger, which caused a lot of destruction there. Mike and Carol got into an argument about each other's pets and Cindy was later crying over the cat. After the events of this episode, Fluffy was never seen or mentioned again.