We’ve just flown for the first time with our baby, shes four months old (and a six year old).
We chose a night flight, she sleeps fairly well between 8pm and about 2am, so we hoped she would during the flight. She was awake at the airport, I think it was the noise and the bright lights, but she did still settle well and slept throughout the flight. She had her dummy during take off, but after that she slept.
We bought her a seat so we had more room, we booked seats near the back so if she wouldn’t settle there was plenty room to walk around with her without disturbing anyone.
As we flew at night she was dressed for bed, so pjs and her sleeping bag, with spares of both.
Double check the baby change in the aeroplane toilet before you need to use it, the one on the plane we were on didn’t have any straps at all, it didn’t even have a lip near the edge. It was also very very narrow, so the slightest roll would have resulted in a fall, so you have to change at a weird angle and stand in a way to use your body as a barrier, especially when you’re bagging the old nappy etc.