C.S.
let me start by saying that I have traveled with three kids plus two car seats on my own across the country so i know that the scariest part is the advance worrying about how you will handle it. but actually, if you use airport resources, it's not that hard. here's what I recommend:
choice 1 (easiest choice)
have your hubby (or a friend) take you to the airport and get a special pass so he can walk with you through security and all the way to the gate. All you have to do is ask at check-in and the personnel working there can print one out for him. (he will need to show a driver's license or pother photo ID). you deal with the baby, he deals with the stuff and it's a piece of cake.
if, for whatever reason they don't give you a pass or he can't stay, ask them to have you met right after security by one of those drivable carts used to drive the elderly and disabled to the gate. have him help you at least up to the security gate. go to the special entrance that is for the physically disabled so you won't have to wait in a long line. Once you get through security, your ride will be right there (you might have to wait a few minutes or even ask twice, but they will come) and you can easily ride with the baby and all your stuff all the way to the gate. plus, your baby will love riding on this cart!
When you get close to your destination, ask the flight attendants to have airport personnel waiting with a cart again at the other side. they will pick you right up at the gate and give you a ride all the way to the outer area where you can be met by relatives.
The hardest part will be getting your stuff up and down the ramp and on/off the plane. 9 times out of 10 other passengers will offer to help you. since you can leave the stroller at the door at the bottom of the ramp, then you only have the car seat, the baby and the diaper bag. If no one offers, ASK the flight attendants to carry the car seat down the plane aisle for you. they may take a while, but they can't really turn you down. so you only have to take the baby and the bag onto (and off) the plane yourself. voila!
choice 2 (good if you like to work independently)
put the kid in an ergo or any other carrier that allows the baby to stay securely on your back. then, use the stroller to hold the car seat and diaper bag and whatever other stuff you have to carry and push it all. Do this in both directions. This is the best way if you want to get around independently, and very easy if you have only one kid.
Good luck!