I cannot give you a comprehensive response due to a lack of available time, but let me quickly a couple smidgeons of a great deal I know about this subject. Let me also be upfront with you that I am vegan by life style choice for my own health, the well-being of the creation, and of course for the sake of the animals.
Do animals have souls? Yes, but they are not the same relationally as we are to Christ. The Scriptures do have one reference about their souls going into the earth, but I think this is more about spiritual relationship than a statement that they dont have souls. Do a keyword search of references of animals in the Bible, and you will see they have capacities we humans like to think they dont have because we, that is most of mankind, savagely exploit them. They sometimes, for example, are better at perceiving spiritual realities than humans.
I have a doctorate in psychology and study consciousness as it is taught in different traditions, can be experienced in different states of consciousness, and can be known through comparative zoological studies of consciousness in animals. Animals can count, think, use video games, call each other by name, and draw (this is established for some, but not all species). It is possible to experience them as much like St. Francis did. I am not saying what St. Francis wasnt miraculous, but there are phenomena that can be observed that say obviously they have consciousness and a different kind of soul just as angels do. Spend the right amount of time in nature with the right kind of consciousness, and you can experience for yourself. Get to know animal activists; they can tell you all kinds of stories. Be brave, and rent/watch the movie The Cove, the dying dolphin seen in the movie doesnt come to the camera and gesture to the humans by accident or human design.
Jesus redeemed all of creation (see Phil. 3:20-21). Gregory is right in what he says. There are many Scriptures that confirm this.
Let us consider the majesty and power of Christs words to us through Paul (1 Cor. 2:9): But, as it is written, eye hath not seen, nor ear heard, neither has entered into the heart of man the things which God has prepared for them that has loved Him. It has entered into my heart I will see my beloved dog Ben in heaven (spiritually at first, then physically). It has entered into my heart that God will compensate all the animals and humans for all the evil that has been perpetrated against them in a millisecond after their deaths; otherwise, this world is emotionally unbearable. I do believe, also, the verse solves the problem of good and evil as we try to comprehend it. Gods glory is that heaven is much better than what I can imagine in my heart. Praise God for that!
When you pray the Glory Be, look at your pets pictures, and tell them spiritually of the glory of Christ, who redeemed all of creation, and He will keep us together forever.
Well, my reports are calling me.
Blessings to all of you.
Then consider an animal that spends its entire life doing exactly what the creator intended for him to do. How can there not be a reward for the animal's good life? Whether this means heaven as we understand it or something else we do not know. I truly believe there is a reward waiting for our pets. I don't have any theory what that reward might be but believe it will be as good for them as heaven is for us. Who knows - it could be the same place!