With a baby, you DEFINITELY want to fly a Japanese airline. The flight attendants care about small kids, the planes are cleaner and it's easier to get a bulkhead bassinet. JAL will even lend you a baby seat if you book a seat for the little one.
When I drag the family to the east coast, we often book an overnight connection at ORD and crash at the airport Hilton. 12 hours in a metal tube trying to calm a baby can be exhausting and it is nice to be able to recharge completely before finishing the journey.