As far as I know, only airline cargo will honor insurance for live animals, not FedEX or UPS. And even with the airlines, it can be really tricky to ever get them to pay up, because they try to find ways to claim it is not their fault.
MOST shippers take responsibility for guaranteeing live arrival. BUT - don't assume anything! Read their terms carefully. Some specifically say "not responsible for carrier error". Then the buyer is out of luck. Others will have terms. For example, I guarantee against FedEx mistakes, but will not guarantee live arrival if you don't sign for the package. That is why I try to avoid home business delivery - they may drop the box in the sun or snow on the front porch, without even knocking on the door. So it is the buyer's responsibility to catch them and sign for it, or better yet, go pick it up at the FedEx office.
So read carefully, and if you don't like the terms and conditions, buy elsewhere.