Pilots N Paws +1 but . . . . . .
. . . . Pilots N Paws is generally about flying RESCUED dogs/cats etc to rescue organizations, fosters, and sometimes forever homes. It is a charitable thing so there aren't charges. Doesn't mean that several someones wouldn't be willing to donate their flying time to just be a delivery service - but they will probably be harder to find.
I have personally done quite a few PnP flights - and one of this length would probably involve at least 3 legs or more (3 pilots/planes).
Have you looked into UPS or FedEx? Apparently they have special provisions for shipping live animals.
2022 =VAF= Dues PAID . . . . .
RV-7 N528DP slow build
First Flight July 26th, 2014
886 hours and counting . . . .
32 Pilots N Paws Flights
Now based at Moontown (3M5)