Where does the Bible say animals must be born again? Would you not include them in the rest of creation that fell as a direct result of man's transgression against God? When God created them, He said they were good. They have His breath in them to animate them, just as we do.
For the creation waits with eager longing for the revealing of the sons of God. For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope that the creation itself will be set free from its bondage to corruption and obtain the freedom of the glory of the children of God.