My DH is a pilot too, and people are always asking him about this.
We have a special bag for the baby's seat, and we check it. She wouldn't sit in it on a plane anyway, and she's still young enough to be a lap baby. (I can't imagine buying a ticket for a baby - that can get expensive if you have a whole family going along. The airlines don't seem to be offering discounted fares for kids anymore.) We've checked this seat at least 8 or 9 times (probably more - it's been used for both kids), and it's never even gotten a scratch. We also take along a "travel carseat" for Alex, but it gets checked too - he's big enough at 3 1/2 to sit in a regular seat with a lap belt.
Take along "quiet activities" and be sure to carry on water and snacks. Muy importante! I always try to plan flights during nap times, if at all possible - it makes the whole event much more bearable.
