Animals do have souls. The Hebrew translated "living creatures" in Genesis is the same that's translated as soul with regard to humans. However, that doesn't really matter in this case, as to my knowledge there's no passage which says that creatures with souls necessarily go to heaven, or that a soul is a requirement to go to heaven.
Personally I believe that there is a place for animals in the next life, based on:
Romans 8
20 For the creation was subjected to futility, not willingly, but because of Him who subjected it in hope; 21 because the creation itself also will be delivered from the bondage of corruption into the glorious liberty of the children of God.
Creation itself is saved, and animals are part of creation.
Personally I believe that there is a place for animals in the next life, based on:
Romans 8
20 For the creation was subjected to futility, not willingly, but because of Him who subjected it in hope; 21 because the creation itself also will be delivered from the bondage of corruption into the glorious liberty of the children of God.
Creation itself is saved, and animals are part of creation.
