animals dont have souls that transcend the capabilities of matter (love, reason, et cetera), so there's no reason to believe that their souls are immortal. We do acknowledge that animals (and plants) have souls, but not eternal souls.
That doesn't mean that we wont enjoy the company of our animal friends in the next life though. Also, St. Francis of Asissi was reknowned for giving sermons to sparrows and other animals, and being more devoted to the subject, he might of had a better understanding of them then I do.