My DD is now 9, but has traveled with me on planes alone since she was 6 weeks old. Before she was 1, she had been up & down the east coast 4 or 5 times, and to London. I fly all the time for my job, and I take her with me when schedules permit. She probably flies 10-15 times per year, and loves it.
Here is my tried-and-true advice, and I hope it works for you.
First of all, if you did not buy her a seat, please reconsider. Babies do much better in their car seats than on laps, and there are many important safety reasons why she should be strapped in. If you cannot swing it, and you are not on SW, then you still may be able to use your seat if there is no one in the seat next to you. When you check in for your flight, ask the agent if there is anyone in the row with you, and if not, ask if they can "soft block" that empty seat. Do not give up your car seat to check. When you get to the gate, go thru the same routine. If they tell you that they can't help you, pre-board if you wish. You will leave your stroller and car seat at the end of the ramp to the plane, and you will pick them up there at your destination. (BTW - I did not take pre-boarding bc I was always worried that if we got delayed, I would have just prolonged the trip. I used to board toward the end, but I was able to do that bc I did not need to use overhead space. ) If they tell you that you'll have an empty seat, then you got lucky and will be able to put your baby in her car seat.
With a 9 month old, I would not take the bulkhead because there is no place to store your stuff (no seat in front of you) so everything must be stowed in an overhead bin. Once they close those plane doors, you cannot get your bag until the pilot turns off the seatbelt sign. If there is turbulence, then you could be stuck for awhile. (ps: There are very few, if any, US airlines that offer the baby cot. We got one on British Airways, but have never seen one since.)
I agree with BevS97, that getting to your seat can be a pain, esp. if you have the car seat, so my advice is to pack as lightly as possible. I was not a Snugli or baby backpack fan, they hurt my shoulders & back (I am very short, too, so they were very awkward for me.) I did, however, master the "Poor Pitiful Me" look, and depended on the kindness of strangers.
Make sure you bring something for her to suck on during take off & landing. I nursed my DD and could not have cared less if my neighbor was uncomfortable with it! But you could use a pacifier or bottle as long as you have something....
I promise that the time will pass quickly, and if she is fussy, keep in mind that you'll never see any of those people again!
Last, FriendsOfEeyore , DD & I fly 1st a lot bc of my travels, I get bumped up. Since your DS will be well-behaved, no one will care... And if you get any attitude, see above.
Allison