Re: Minimum baby age?
Our daughter was born at 34 weeks unexpectedly while my wife was on a job interview. (Fortunately, I was along to carry the luggage.) The pediatrician attending the delivery suggested we fly home (2.5 hr fllight) the next day. (Other than being 2.1 kg, she was healthy, with good lungs and adequate thermoregulation.) His concern was that she was likely to develop jaundice of the newborn, in which case she'd need to be treated with bili-lights for a week or more, in a city that was far from our home, before we could fly. The airline was fine with her flying (with MD's note), the flight was uneventful, the cabin crew were very kind to us as new parents, and she did develop jaundice two days after we returned home.
Fourteen years later she's none the worse for it and still loves to fly.
PS. My wife went down later to complete the interview and was offered the position.