The Giant Moon Rat is non-anthropomorphic rat or rat-like creature which was temporarily mutated into a monstrous form.
This mutated the unsuspecting rodent to an enormous size, and gave it the ability to teleport and travel at enhanced speeds. Scrooge McDuck, searching for the Green Cheese, encountered the now-enormous rat and fought it. Now subdued, the rat morphed back into its un-mutated state, and the Cheese reappeared unscathed. The rat then ran off to parts unknown.
How the rat managed to survive on the Moon is unknown, although it is possible that it does not originate from Earth, or had already been mutated to have the ability to breathe there by the aliens which had captured it.