Mad Max had his dog.
The Beastmaster had a pair of ferrets named Kodo and Podo (and a hawk and a panther).
In the Walkabout convention playtests, I gave one of the pre-generated characters a blank-slate companion animal. Two players took this character, and for their companion animal one claimed a marsupial lion, the other was very tempted by the idea of a companion "Drop Bear". The reasoning in both cases stated that if spirits had returned to the earth, then the totem animals and nightmarish beasts of the past had probably also returned. Since the shape of the animal didn't really make any mechanical difference, I let these creatures into the game. It made for great flavour.
But what other types of animals might a post apocalyptic wanderer want by their side?