We flew with my daughter when she was 13 weeks and she was great. Our pediatrician told us it is easier at 3 months than 18 months too. She had her own seat, which she used for takeoff, landing, and turbulent parts of the flighs.
Our friend's baby was due July 5th, they flew to visit family in Utah in early May, stayed till June, went to her old OB out there and found out her water was about to break, had the baby in Utah on June 21 and flew back to DC with him on June 28.