Flubble

The Flubble was a type of creature somewhat like a Koala with six legs and a smaller nose. The First Doctor had a pet flubble under his bed while he was still in the Time Lord Academy, though he was nearly caught when she came into heat and starting using her mating call. (PDA: Island of Death)


 * Since the Doctor was still in the Academy, it would suggest the flubble is native to Gallifrey. Of course, due to the Time Lord's abilities, they could potentially get creatures from any point in time or space.