Hi M. -
I haven't traveled with my son, yet, on a plane, but here is advice I have heard about -
Cabin pressure - if your baby is sleeping during takeoff or landing, she might just continue to sleep through it. If not, try to nurse her or give her a bottle. The sucking and swallowing will keep her ears open. In this respect, a 4-month old might be a little easier to travel with than an older baby or a toddler. : )
If you are thirstier from the dry air, chances are your baby is, too. But if you feed her during take-off and landing, that should help. Maybe also bring some water in a bottle to keep her hydrated and in case she's not in the mood for breastmilk or formula.
What to bring - as little as possible. You know how crowded planes are! However, do bring the basics. Bottle(s), diapers, extra clothes, a blankie, and a couple of her favorite toys to keep her entertained. If she's a good sleeper, she might sleep through it all, so don't forget a book or magazine for yourself, too. Or just try to catch a nap! Tip - I once saw the flight attendants reheat a bottle using the hot water from the coffee machine. They put hot water in a clean air-sick bag with the bottle. Worked well, and then they didn't have to worry about the water being purified to mix in the bottle.
Security - Hopefully you're not traveling alone, and someone can help you carry everything through security. You can usually bring a stroller right up to the door of the plane and check it there, but you'll have to carry your daughter through security, so have the stroller ready to collapse and put on the belt. Again, travel as lightly as you can, but bring all the essentials.
Hope that's helpful and not too much of a repeat of things you've already heard! Good luck!