I flew with my daughter a couple times around that age! My tips are

bring what you need for the plane and enough for a few hours extra in case of delays

get a new toy baby has not seen for the plane

bring liquid formula to avoid mixing and such( make sure the bottle is clear and they can put it through a machine and not have to open them)(I used the small 8oz enfamil ones)

if she is eating any solids such as puffs bring new flavors in snack size baggies for quick easy distractions

Make sure the airline knows you are bringing a baby(call and add to reservation for free and they will try to sit you next to an open seat) and check in online early)

try to keep baby up through a nap so they will sleep on the plane

Make sure they are hungry for takeoff and hopefully landing in order so they will drink a bottle so babies ears don't hurt!

I would take a few diapers, wipes, her bottles, the formula, an extra outfit, a water bottle and toy(s). I'd usually take two bottles with just water and then add formula before I board. Security can be a hassle sometimes and test the water and formula but they'll let you take it all. My daughter would sleep through the flight. I think the most nerve wrecking thing is security besides that it should go smooth :) unless baby is like mine and decides to poop herself to the point where it comes out before boarding EVERYTIME lol

she would be free. I took my son to mexico and paid a small fee for him to sit in his car seat just to be on the safe side. probably like 25$ it was like 2 years not quite sure.

children under 1 or 2 are free because they are able to sit on your lap, so you don't need to pay for another seat. you can bring the car seat and stroller but those would be put away with the luggage under the plane. and only pack what you would need in the diaper bag, bottles, diapers, extra outfit or two, and a toy maybe.