Scooby-Doo and Scrappy-Doo Season 4 Episode 13 Who's Scooby-Doo? ( Air Date 1982-10-23 ) Genre Animation, Mystery, Comedy, Family, Kids category. Overview "Scooby and Shaggy switch bodies thanks to a machine at a Science Fair, but they can't switch back because someone steals the machine and they try to find it.".