There are Yahoo groups for rescue transport along every major interstate in the country. I would contact some of the coordinators for the primary routes, ie., I-30, I-40, and see if one of them would put together and moderate the trip for you if no one in your group is familiar with the process.
I-30_Rescue_and_Transport : I-30 Rescue and Transport
I-40_Trans_CA_2_NC : I-40_CA_2_NC
It would most likely have to be a three day transport, starting on a Friday and continuing on Saturday and Sunday since it is a long trip. But the dog should do fine. Years ago I helped a Katrina dog get from her foster home in VA back down to TX and she was an old gal, 10 or 11. She'd been away from her family for nearly a year and when she finally reached her destination she forgot that she was an old dog and practically was doing back flips over being reunited with her long term family who'd had her from puppyhood.
Best of luck to you and the dog.