I really don't know. If you want my opinion, I would say... "kind of". I think animals have a soul on this earth in that they are more than just "machines"...there is a spritual life in them, they can have loving relationships with each other and with us, and with God as his living creation, and they should be treated with respect. However, I don't think that animals have eternal souls in the same way that people do.

Just my thoughts. It's really a mystery, and I have no certain answer.