Nice play on words.
Muppet is the term used for a soft toy-like puppet, like those in Jim Henson's The Muppet Show. Elmo, mentioned above, is a muppet. So are Kermit and the Cookie Monster.
The derogatory usage referring to humans of low intellect is similar to the usage of the word 'dummy' since muppets, too, are dummies.
Moppet = cute girl child. Think Shirley Temple in her earlier roles.