flying with a 2 month old

Any tips for a flight with a 2 month old baby? i am taking a 2hr flight and am a bit nervous.Also i know you can take a stroller but mine is a travel system so im taking the carseat with it too would they charge me extra even tho i wont be putting her in the carseat for the plane ride? she will be on my lap because i didn’t feel the need to purchase another sear ticket for her.