I could be wrong, but I don't think Mormons believe we'll have our pets in the after life. They don't get raised from the dead.
But if the whole thing about exaltation and eternal progression are true, then there are at least some people who will become exactly like Heavenly Father, meaning they will have all of his powers and abilities.
I don't know about Mormons, but in ordinary Christian theology, God is all powerful. He can bring anything that's dead back to life. So it seems like if Mormonism is true, then some people can get their pets back. Eventually.
