I'm adopting out of state, and will be flying home with my baby when he is 7-10 days old. It will be a 4-5 hour flight on Southwest or Alaska. What car seat recommendations can anyone give? Should I bring the car seat base with me, or strap in the carrier itself? I was planning to purchase a Britax B-Safe or a Chicco Keyfit 30, but I have no idea how these will fare on an airplane!