A pet-shipping service is a good idea, but I’m not too fond of the no-humans policy.
We had to ship our three (at the time) cats from California to Virginia. It was very traumatic for them, and it was very hard for me and Hubby to see them so upset. But they got there in good time, and the service included door-to-door delivery. They all survived the flight, but I think it would have been better if we both could have accompanied them on the plane and in the same cabin. It just wasn’t possible at the time.
(Hubby was in Virginia at his new job, and I was in California packing.)