You can carry your baby aboard the plane if you don't want to have her in a car seat for the trip or haven't bought a ticket for her. Bring your own car seat and send it through with the baggage. It's the only way to ensure that you are going to use a safe car seat for the trip. You can either remove the cover, send it through in the original box, or you can buy a carrier cover that will protect it from damage. Hold her on your lap for takeoff and landing, and be sure to either nurse or bottle feed while this is going on.
If the baby has a cold, it's best not to take her because the excess fluids will either make her very much in pain or give her permanent damage. Just be sure to get the OK from your doctor or pediatrician before your flight.
Remember that you can't be too prepared. Bring a tote with plenty of diapers and wipes, a couple changes of clothes and blankets. You never know when she will get a soiled diaper that leaks, spits up significantly to ruin her clothes...and maybe even yours.
If you have her in a sling, you will not be able to keep her in it for the flight.
If you have any other questions, feel free to ask.