Okay, I hear this question a lot as a vet tech, especially when a beloved pet must be euthanized due to an incurable illness that has progressed to the point where the animal can no longer be relieved of suffering through medical means.
My answer to the client is as follows, “I believe that Heaven is a place of absolute joy, and God wants us to be happy in Heaven. Therefore, I believe that God, in His infinite Mercy and Love, will do whatever it takes to ensure that we are happy. If He knows that having a beloved pet in Heaven is what it will take to make one of His children happy in Heaven, then that pet will be there.” And I leave it at that. Most every client seems to be comforted with that reply. Because we have clients of many denominations (or of no particular denomination but simply ‘believers’), I keep it very general.
I do believe that animals go to Heaven-- but not sure “where” in Heaven, if there’s a special place where animals go, or anything like that, because I don’t know what Heaven is really like since I haven’t been there yet. My pastor explained that an animal’s soul isn’t the same as a human’s. They have a temporal soul, but it doesn’t live on after physical death the way a human’s does. But his belief, and HIS PERSONAL belief only (not official Catholic teaching), is that they might possess a different sort of ‘spirit’ created by God and that only God knows, which returns to heaven, But it’s not a permanent soul like that of humans-- but perhaps a sort of ‘energy’ that returns to its source once the bodily host dies. Because God is all-powerful, He can restore the body in a form that we will recognize once we return to Him in Heaven after we die, and the ‘energy’ is then instilled into the ‘heavenly body’ of that beloved pet. After all, God created the pet on Earth; why could He not recreate that pet in Heaven?
Pope John Paul II taught love for animals more than any other pope in recent memory.
In 1990, His Holiness proclaimed that “the animals possess a soul and men must love and feel solidarity with our smaller brethren.” He went on to say that all animals are “fruit of the creative action of the Holy Spirit and merit respect” and that they are “as near to God as men are.” (referenced here…
thecatholicpriest.com/Popes_on_Pets.html). That doesn’t mean that the yhave the same KIND of soul as a human, but they do have a soul nonetheless.
As for purgatory, since animals really don’t have a concept of ‘right’ or ‘wrong’ or ‘reason’, they can’t sin. So, IMO and understanding of the matter, they wouldn’t have a need to go to purgatory or Hell (well… except maybe fire ants!

).
In short, if God wants His animal creations to be in Heaven, then they will be there. And since animals bring so many people joy, and since God wants us to be happy in Heaven, then by that logic, it would stand to reason that animals would go to Heaven.
~In Christ,
Spoken4