Flying a 35 weeks and 36 weeks

So I'm 31 weeks and 4 days today, but I will be going back home soon to see family since we're military and literally only see them like once a year. Anyway my husband and I are gonna be flying, I will be 35w 2d when we leave and 36w 2d when we come back. Has anyone flown around this many weeks? I'm getting pretty nervous about it, my doctor said that they'll check me the day before we fly off to make sure everything is ok and give me all my paper hospital work incase I have to deliver as an emergency over there (which of course I hope I dont). Anyone with any positive feedback would make me feel so much better. Also just an FYI, I did check with the airlines and it said as long as I have a doctor's note saying I'm ok to fly after 36 weeks, (which will be when I'll be flying back) that they'll let me board.