Personally I think so... The Bible speaks of animals in heaven so why wouldn't animals on earth have souls that go to heaven?
I also like to think of it this way; humans, animals, and plants, are all considered organisms but there is a big difference between plants and animals. Plants can't think, make decisions, feel emotions, have individual preferences, connect or have friendships with others. But animals, especially dogs, can.

I would like to think that this indicates that animals have souls.