Try and sort out a flight around nap time, so that they can have a quick top up and drift off to sleep for hopefully the majority of the flight!
We travel all the time, bub was 8 weeks the first time. It's not hard (I actually enjoy the flights) but you need to be organised to make it easier for yourself. Zip lock bags help avoid potential spillages &/or soiled clothing. Thermos bottles help keep water warm if you are formula feeding do that you don't need to rely on flight attendants to help and if you're BF pop em on the boob however many times you like!
If the flight attendants don't give you one straight away, ask for a pillow ASAP as they only have limited supplies of pillows and blankets.
Also if you do need to pull out & pack away stuff, do it before the 'fasten seatbelt' sign goes on so that you are prepared when it's time to get off!