Of course, animals have souls, but they are not “human souls”, but “dog souls”, “cat souls”, etc.
The harder question to answer is whether these animal souls have the same fate as our human souls. Do they go to heaven?
We know we could go to heaven because God told us. Our souls are eternal but our bodies are not. We have eternal life and we need to go to God after this life.
God did not tell us about animals. Many philosophers said that animals cannot have eternal souls so they have no existence beyond this life. That might be so, it might not. We do not know.
What I know, though, is that God created the animals too, and He called them good. And whatever is good is a participation in God. So whatever God’s plan for the animals is, I know for sure that all that we find good in the animals, we will find it perfected in heaven.
So, if you have a pet, all that rejoices your heart, those things that lead you to the awesomeness of God, you will find all of it in heaven a million-fold and more.