Little green ma... moose

Martian moose are small, green and shy (which is the reason why the NASA hasn't found any so far). Their tradition of removing their brains for safekeeping (compare terran practise of putting your heart into a jar to become un-killable) has led to the surprising discovery that brains can live and be bred autonomically from bodies, providing they spend enough time in nutrient solutions. Those brains are favoured pets.

(the image shows an individual named Melvin taking his brain Rover for a walk)