Rose (Rise of the Cybermen)

Rose was the Yorkshire Terrier that belonged to Jackie Tyler in Pete's World. She seemed to be that world's closest thing to a counterpart of Rose Tyler in the Doctor's universe who was Jackie and Pete Tyler's daughter. The alternative universe Jackie and Pete had no children.

Biography
An individual going by the name "ChatGuest1", who seemed to know Jackie well, knew that she had a dog called Rose. (GAME: Cybus Spy)

On 1 February 2007, she was at Jackie's birthday party when the Cybermen attacked. The Tenth Doctor, who along with his universe's Rose was working as catering staff at the time, couldn't help but laugh when he realised his companion's parallel world alternative was a dog, though apologised shortly after. (TV: Rise of the Cybermen) It's unknown what happened to her when the Cybermen attacked but the Doctor declared to Pete "Anyone inside that house is dead." (TV: The Age of Steel)

Other references
The prime Jackie Tyler, feeling lonely as Rose travelled with the Doctor, considered getting a "little dog" which she would have named Rufus. (AUDIO: Wednesdays For Beginners)

In another parallel universe, Jackie Prentice did not have a dog, but named her cat Rose, as she'd always liked the name. (AUDIO: The Endless Night)

Behind the scenes
Rose was played by Tinkerbell.