No animal, apart from man, has landed on the moon as far as is known.
The first animal in space was a dog, but she did not survive. Laika, the Russian space dog, was part Siberian husky. Prior to being enlisted into the Soviet space program, she was a stray on Moscow's streets. On 3 November 1957, Laika was launched into space aboard the Sputnik 2 spacecraft. She was fitted with monitors to check her heartbeat and other vital signs and was reported to be calm during the first hours of the flight.
Evidence released in 2002 indicated that Laika died of stress and overheating within a few hours of launch, despite Russian assertions that she died painlessly when life support gave out after a few days.
According to the book "Turtles and Tortoises for Dummies" by Liz Palika, the Soviet interplanetary probe number 5 carried several Russian tortoises into lunar orbit making them the first vertebrates to circle the moon. This flight took place in October 1968.