In The Muppets' Wizard of Oz, instead of being a dog, Toto is a king prawn, rescued from Aunt Em's Diner by Dorothy since Aunt Em wouldn't allow her to have a dog. He is one of her few friends in Kansas, and she rushes back into the trailer to rescue him during the tornado.
Once transported to Oz, however, Toto, having broken out of his tank, has enlarged, is nude, and speaks with a Spanish accent. Dorothy supplies him with costuming, and he (portrayed by Pepe the King Prawn) tries to become her agent in return.
He is made to look like Dorothy's pet, but doesn't get anymore screen time until very late in Return to Oz. Dorothy's real pet has turned out to be Belinda in the long run. Despite this, Toto is still Dorothy's official pet, since most media, including the Oz franchise, explicitly dismisses Return to Oz from canon.