Begoony
From Muppet Wiki
Begoony is a magical rabbit-like creature who Mokey befriended in the Fraggle Rock episode "The Incredible Shrinking Mokey."
The puppet was later reused in The Muppet Christmas Carol (as the child of Mudwell the Mudbunny and Murray the Minstrel) and in Muppet Treasure Island (as a pirate). On Mopatop's Shop the puppet would be used in various roles among them was the moon creature Clicksnizz.
