I do not believe animals have eternal souls. They cannot learn right from wrong, and do not have moral capability. Yes, you can discipline a dog, but it is only learning that it will be punished if it does a certain thing, and it wants to avoid that. Also, Genesis says "let Us create Man in Our image." I don't think the Bible says anything about animals being created specifically in His image. I don't think animals have anything eternal about them, because their salvation is not mentioned in the Bible, and God did not provide a way for them to be saved, as he did for Man with Jesus. Yes, they can show emotion, but I don't believe that emotion entails a soul.
Just my thoughts.