Welcome to PNP. While it is possible to do, you would better off looking into commercial flights. Your trip is long and would require multiple pilots and lots of coordinating to complete, as well as an overnight most likely.
Have you posted your request under Animals Needing Transport already? One it's posted, you can click on "Map this request" and find the PNP members along you route~~
for pilots &
for ground volunteers. Clicking on the icon will bring up that person's info & you can email or PM them from there. Some people also provide a phone number there. Contacting them directly is recommended for the fastest response as there is no guarantee that the person you need will see your post on the board.
I will also PM you with a ground transport suggestion.