According to Aquinas, animals have a material soul, which “dies” along with the animal. Animals can be resurrected if God willed it, but it wouldn’t be the same “soul” as the one that existed on earth, it would just look and act similar.
Laudato Si, Francis’s encyclical seems to hint at it
“Eternal life will be a shared experience of awe, in which each creature, resplendently transfigured, will take its rightful place and have something to give those poor men and women who will have been liberated once and for all”
What is that creation he is referring to? Animals, plants, rocks, the moon? We don’t know.
My idea is that “no eye has seen, nor ear heard” what we will experience in heaven.