Plastic Little: The Adventures of Captain Tita (1994)

Tita, captain of a pet-hunting ship for the galaxy’s upper class, finds herself babysitting Elysse, a scientist’s daughter being pursued by the military commander Lord Guizel, who’ll stop at nothing to retrieve the key to the high-powered weapon her father created. Dodging the lord’s clutches is a planet-wide game of cat and mouse for Tita and her crew, with one crucial difference: Mice don’t shoot back!