Dorothy Cheney's
Baboon Metaphysics reports that baboon mommies carry around the bodies of their infants that die of disease until they rot and start to disintegrate. (That observation is as close to "metaphysics" as I remember the book getting - it's really about their social skills.) That might be construable as some kind of belief in an afterlife, or hope for a resurrection, or some such. Or that baboon mommies are really dumb.
Dogs and cats, in my experience, don't even take much notice of death of their housemates. They may miss them after they are gone, but my admittedly anthropomorphic read on this is that they are wondering "Where the hell is Fluffy? I want to play!" rather than any deeper thinking on the absence.
Interesting topic, anyway!