What would be the easiest way to fly with a 2 month old?

Ideally I would rather not travel so early with my little one, but with the doctors go-ahead we need to take a weekend trip. The things I need to take are 1 suitcase, car seat, and diaper bag. I am going to be carrying the baby in a sling. I would buy a second ticket and just put him in the car seat next to me but given the holiday tickets are quite expensive. I'm thinking I will just check my suitcase and car seat and just worry about carrying the diaper bag (in addition to him/the sling). The idea is to have as little as possible getting on the plane. It's a 4 hour plane ride. Any pointers, do's and don't, shared experiences, or just any information at all would be appreciated. Thank you!