I think because you have a lap baby you can bring the car seat to the gate in case a seat is freed up for you. It's much better to have the baby in a car seat than on your lap, for a zillion reasons, so take a seat if you can get one. If not they will have to gate check it for you.
You may find that it's easier to check as much as possible when travelling with a baby.
After 9/11 and all the restrictions on carry ons, I felt much lighter & freer while travelling. Packing lightly for the plane makes everything so much easier!