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Muppy
Muppy is a cute white shaggy dog. She belongs to Scooter's uncle, J.P. Grosse. She appears in Episode 101: Juliet Prowse, where She uses his connections to make demands on Kermit. She made a number of background appearances in season 1. Her last appearances included the wedding scene in The Muppets Take Manhattan and the pet care center detention hall scene in The Muppets at Walt Disney World.
The original "fluffy white dog" puppet was Rufus, in the 1970 fairytale special Hey Cinderella. The puppet was rebuilt for The Muppet Show with a more realistic looking face, so that a real dog could play her in long shots. (The producers used the same trick a few years later with Foo-Foo.)