In the bible, animals have souls. I believe that they have a special heaven for them. But it probably is down in the earth somewhere. Before Jesus raised from the dead, Paradise was down in the earth in Abraham's bosom also. But when the atonement was made for sin by the Lamb of God, Jesus Christ. Then those in Paradise ascended to the 3rd heaven.
The reason being is that when we receive Jesus atonement for our sins, we are born of the Spirit. And become spiritual souls. We are a trinity again; body, soul & spirit. In the beginning Adam was a body, soul & spirit. But the day they ate of the forbidden fruit, came spiritual death, then physical death. So the soul went where the Lord put the soul.
In the OT, the High Priest would make an animal sacrifice for the peoples sins each year. And so their sins were covered, but they weren't born of the Spirit yet. Not until the Lamb of God paid for our sins on the cross & since He was without sin, raised from the dead. He overcame the original curse of sin & death.
So?
Whenever I have asked God about my pets, I know that their little souls go some place special. And probably are going to be part of the new heaven & the new earth.