Hi M. S! i've flown extensively with my son from the time he was 2 weeks old to 2 1/2 years old so i know air travel with a baby pretty well now. first of all, let me pass on to you what my older sister, and mother of 4, told me: "you will never have an easier time traveling with your child than when they are a baby!" So, take comfort in that! You will find this trip surprisingly easy!!
i invested in one of those travel strollers that converts into a car seat and it was a wonderful way to move thru the airport with ease. we often checked the stroller right at the gate and it would be there on the platform at our arrival gate! my son is almost 3 and we still use that convertible stroller every time we travel. it works great as a car seat when you have to rent a car when you land.
At your baby's young age the infant car seat is still an easy way to hand carry your baby thru the airport. Most airlines let you take the baby in the infant car seat carrier right into the plane. Then they usually have you take the baby out and put him in your lap for the flight and they'll store the car seat in the overhead compartments. Your little one will love resting on your lap and will sleep like an angel for a good portion of the flight!
I also always travel with a small bag of toys. but be careful to choose toys,rattles, soft books that wont roll down the aisle or get lost! Always fly with 2 changes of clothes or so-babies have unbelievably inconvenient timing for diaper accidents! : ) And invest in a pair of shoe-socks that really stay on their little feet-regular socks fall right off their feet too easily.
My pediatrician also gave us the advice to always make sure our baby was feeding or sucking on a pacifier for take off and landing. it helps their ears to adjust to the pressure changes in the cabin.
Have fun!! your baby will be a breeze!!!