Each time I have flown with my now 20-month old I felt like I had run a marathon by the time we settled into our seats on the plane! However, it does get easier when you know what to expect. You're going to do great. Here's my best advice:
1. Take carseat to the gate. If there is an extra seat on the plane, they'll actually let you use the carseat on the plane, and your lap will even get a rest. Tell the attendant at the gate that you have a lap child and ask if it is a full flight. If not, she'll switch your seating so you can strap the seat in right next to you. If it is a full flight, they'll simply tag the seat and take it from you on the concourse (down the ramp, just before you get on the plane). You will have to have the carseat wherever you're going, so this works out well. Since it is an infant seat, you can probably use it without the base. Check the instructions, and practice:)
2. Stoller: As with the carseat, they'll let you wheel it right up to the door of the airplane. Be sure you get a Vallet Tag when you arrive at the gate. You'll break it down and they'll put it in the compartment just under the plane (with your carseat, wheelchairs, etc). When you arrive at your destination, they'll bring it right up to you where you step off of the plane. It's really nice! I advise that you just be prepared to break it down quickly, so as not to hold up too many people. Sounds like someone is traveling with you, so just plan out who will do what and it will be easy.
3. Carry on: Pack light. I would either take a big purse that serves also as the diaper bag, or vise versa. At your baby's age, he will not need a lot of gear. Take plenty of diapers, wet-wipes (to sterilize the plane, hands, and anything that touches that nasty floor!) and be prepared to nurse him or give him a bottle, hopefully at take off or landing (to help his ears). He will probably be mesmerised by the new environment, sounds, people, etc. Take a book and small toy. The flight will be a great bonding time for you all--very close quarters and constant interaction! If you're lucky, he'll sleep a good bit.
4. Disapproving people: Babies cry, they take up room, and their moms take longer getting on the plane. That's life. Most people understnad it, and some are actually eager to help. The few who don't are just self-absorbed, don't have kids, or are generally bad people. No one on the plane is going to get to the destination any faster than anyone else, so a small delay getting to their seat is not going to kill them. Take a deep breath, do the best you can, and just smile sympathetically at others who may be inconvenienced by you. Let people go around you at security when you're piling all of your stuff (car seat and broken down stroller too) onto the belt. I wish I could take that advice totally, but it is still nerve racking, I'll admit! Be sure you have all of your liquids, INCLUDING DIAPER CREAM AND BABY FOOD/FORMULA in plastic bags for security. You can't take anything in in a sippy cup.
Good luck! You'll do great. I'll bet the return flight is 100 times easier.