Yes all things have a soul even the trees of the field have a soul toward their Maker. God made all of the birds, the cats and the dogs and yes I believe they have a soul.
Animals are able to understand commands and love. They often crave love. They would not understand love if they had no soul.
I believe we shall have pets in Heaven including those we fear here. We shall have nothing to fear there. Not all animals are edible and therefore have another purpose.
GOD is a loving God and He would not give us something to love if we cannot have them in Eternity. Before King David was a king he was a shepherd of sheep. The lowly shepherd became king. The king Jesus became a lowly shepherd, and He became a lamb. The whole world has the grace to be saved because the King became a Lamb.
Thank you... Beautiful post.