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