I'm a former Flight Attendant and I fly a lot with my children.
When mine were small, I used a baby carrier and it was never considered an "extra" carry on. It's just like the clothes the baby is wearing and takes up less room than an adults' coat, which also doesn't count. It was never questioned and I've never heard of one being considered a carry-on.
I do recommend a really good carrier that you can sit down with and if necessary, can be used as a breastfeeding cover-up. Fiddly front packs like the Bjorn are not good for your back and the baby's and are not very convenient for flying. Make sure it's a good quality carrier like a wrap, sling, mei tai, front/back carrier, etc. For more information, there are a couple of site with multiple company products you might want to check out:
http://peppermint.com
http://kangarookorner.com
Do you need your car seat at your destination? Be sure to not check it in as luggage, It could too easily be lost and/or broken in transit. Ask nicely at check-in if it's possible to have a free seat to use your car seat on board. They often do this for families.
Even if you are unsuccessful in getting a free seat, take your car seat to the gate of the airplane and have it gate-checked with the stroller. You can use your stroller to transport it (perhaps with a bungee cord or if it's a travel system, they go together anyway). This is much safer than checking the car seat as luggage.
Not only will your baby be much safer in a car seat but it will be a more comfortable flight for you both.
If your baby does end up on your lap, be sure s/he is LOOSE in your lap for take-off and landing. It's very dangerous to have the baby attached to you in any form, including in a carrier. You can simply loosen the carrier and flip it over your head (especially if the baby is sleeping).
Be aware that usually security does not require removing the baby from the carrier. I've had them "hand check" a sleeping baby going through. If they're awake, they're more likely to ask you to take it off and put it through the X-ray.
Please not that it is a myth that babies need to suck on take-off and landing. If your baby is in his/her seat, don't remove them during these times. Keep him or her in the seat. No need to introduce a pacifier or bottle if your baby doesn't normally use them. Also, babies often fall asleep on the taxi to the runway so don't wake your baby up unnecessarily to make him or her suck. If you're concerned about ears, visit the doctor before leaving and be sure there is no infection or other problem. Healthy ears can handle pressurization. I never had any problems with any of my children and their many flights and I rarely saw it at work. It is an over rated problem (please don't let your baby cry, claiming it is "his ears" when it is probably something else-seen that!)
Feed your baby when he or she is hungry and don't force it at other times.
The AAP only recommends that the baby be awake at the TOP of descent (landing is too late). This is about an hour before landing.
http://www.aap.org/patiented/flyingbaby.htm
For more information, nine years ago I wrote an article on this subject. It's based on both my personal and professional experience of flying with children. It's totally non-commercial and other parents from around the world have contributed;
http://flyingwithchildren1.blogspot.com
Have a good flight!