Another good thing about going out there and flying back with the pup is you get to see and meet mom. That's pretty informative, I think.
I've flown dogs as cargo and not had any problems. I've also flown with them as baggage and not had any problems. I don't believe there is a price difference for a pet ticket between cabin/baggage, and the last time I flew with Dillbird, his ticket was $75 each way. The size of the under-seat carrier is small- the pup diefinitely couldn't sit or stand.
Nanci