It's all up too your dr. I just went this morning and my dr said since I don't smoke drink I have a normal weight Gain and the baby is fine I'd be able to travel up to 37 weeks. But after that they wouldn't allow it just in case. I'd get a note from your dr just in case they try to give you and trouble.
Most airlines will require a note from your dr saying it's okay for you to fly.
I wouldn't though. ...
But imagine going into labor in a plain!
No most airlines won't let you on a plane after 35 weeks I'm sorry hun