Hi N....here is a version of my response to this same question a few months ago...
I have flown a lot with my little boy by myself and it has always been a pleasure but has always been a lot of work! I am flying again on Monday! He is now 21 months.
I always put him off for a nursing (bottle feeding) until we are taxiing down the runway--this way he'll be sucking and his ears don't bother him with the pressure changes. Same thing on the descent. You can also give a pacifier if that's your bag. That's the part that bothers most of your fellow passengers--the baby is crying because his ears hurt!
The whole giving your little one benadryl thing is creepy if you ask me. Drugs act more potently in lower air pressure so be very careful and get a physician's advice on dosing if you want to go this route. I think under 2 is too young.
Snacks are good. Kids love the tray that goes up and down--so if you don't get a bulkhead row (absolutely the best place to fly with a baby) then don't fret it. I agree that you should try to ask for help with your fellow passengers to get you more room. 2 seats are crucial with changing diapers. Your husband will have to vacate his seat while you change your little one. Your only other option is changing on the floor in front of the bathroom (ew!). Don't worry about other passengers' reactions to diaper smells--just do it and seal that dirty diaper off as soon as possible in a plastic bag! Warn your seatmates about the impending change and give them a chance to vacate their seats for a few minutes. "If you want to stretch your legs, now's a good time because I need to give the baby a change!" Try to time changes at the best times: not just before meals, not during the movie etc.
When you get to the gate, ask the gate attendant what the loads are on the plane. If they have many extra seats, then when you get on the plane, you'll have a chance to move around to try to get two together after everyone is seated, but before the plane starts moving. Try to at least get an aisle seat so you can get out easily.
Bulkhead seating is great because you can stand with your baby there, once the flight has leveled off. You can "fly " your baby around. You can pick out all of the older matrons who think your daughter is adorable and wave at them. So many people will wave back! Just act like it is fun and have a good time and everyone else will start loving your babe.
Keep up a conversation with your baby about everything that is going on in the plane. Name everything. Introduce her to anyone that looks interested and tell them about your babe.
Great toys/entertainment:
a cloth napkin that you can play peekaboo with and make into animal shapes over your hand (rabbit, bird etc.)
a sock puppet or two that you can hold dialogs with
a small car
a small baby doll
a quiet rattle
lap games (pat-a-cake, rhymes, claps, pointing to body parts etc.)--get a book, ask friends or make them up!
songs with gestures
Finally: walking the baby. Take turns with your hubby. People love seeing a baby parade up and down. Try to do it when there is no movie but if you have to, do it anyway. Do not do this while the carts are out and serving people unless your timing is very good or there are enough empty seats that you can scootch into!
Have fun! You may be pleasantly surprised! Your babe may be intimidated by her surroundings and not want to get away from you after all. Have a great trip!
S.