Humans are spirit, body and soul. Animals are body and soul. They have no spirit.
Your soul is who you are. It's how you feel emotions. Animals can be emotional - they have souls.
Leviticus 11 has an exhaustive list of animals.
God spoke. He spoke animals into existence in the beginning. God handmade humans and breathed life into them. I don't think pets go to Heaven.
Will there be animals in Heaven?
There may be animals in Heaven. They were in the perfect garden of Eden before it was imperfect. Because God is restoring things back to perfection, maybe the animals from the garden will be in Heaven. But if our pets do get to Heaven, that would be so cool!
In conclusion, really, I think the animals that existed in the perfect beginning , before the world was bad, might be in Heaven. But maybe its not the same with pets. Possibly, it could be. God knows. He has a plan!