I would never put a dog you care about in the baggage hold of a airliner. To many things can go wrong and even if it goes well it’s traumatic for the dog.
The only option is to declare that you are disabled and get a fake ESA certificate to bring the dog in the cabin. Your personal level of integrity will have to guide you on this. So many people have abused this privilege that it may go away soon. Sad for the few that actually needed it.
G