I think you have 2 options. A air transport. B set up a car transport.

A. I only have limited (one time) experience with air. I adopted a dog from a rescue group, she was in Ohio, I am in Rhode Island. The rescue set up the transport. The dog flew priority cargo, which is the pressurized part of the cargo bay. American Airlines from Ohio to Chicago's Ohare, the American Air Express to T F Green in Providence.
I was billed: the adoption fee
- fee for air approved carrier $50
-fee for flight $175
- fee for vet approval and for Ohio Dept of Agriculture form.

the vet certificate is good for 10 days, so the exam must be within 10 days of the flight. I can tell you lots more if this is the method you are thinking about. Let me know.

B. I have no experience with car transport except what I have observed here on Pet Talk. The route is set up with legs of 400 to 500 miles with stop overs and change points. The pet is transferred from vehicle to vehicle. I think the search function will help you find someone who posted asking for volunteers, and then you could ask that person directly.