J.,
#1 - Make sure you have a seat on the right hand side of the plane if you did not buy your baby a ticket. They only put the extra oxygen mask on the right side of the plane and if the attendant sees you sitting on the left with an infant on your lap, she will make you change seats with someone. It has happened to us and it is a pain. Also make sure you don't have a seat in or next to an exit row. They will make you move for that, too.
To get through security, ask for help. The security people want you through there as fast as you do, just ask them to hold something or reopen the stroller or whatever you need. Bring an umbrella stroller that she can sit in while your hands are full. (You will have to take her out and put it on the xray machine.) You can check the stroller at the gate so you have it with you in the airport. FYI - when I went through in December, all 4 of my kids had to take off their shoes and they wouldn't let you bring water through security; have to buy it in the airport. Wear slip ons.
I would sit at the back of the plane. It is closer to the bathrooms, you get on first no matter the boarding policy, and it is noisier back there. Good white noise for baby and good for drowning out her screaming if it is a bad flight. :) When the attendants aren't busy, they play with the babies back there and sometimes a new face keeps them happy. Also, you can ask for a preboarding flight because you are traveling with an infant. (Some airlines will let you do it and some won't.)
Good luck,
S.
If your baby is upset, just stay calm and ignore any rude comments of fellow passangers. A bottle, nursing or binky are your best bets; just do your best and most people will be supportive and understanding.