Just to preach to the choir, but don't worry too much--it's not soo bad.
I recently did an 18hr direct flight (yes, they have those!) with my 6 mo old by myself and it wasn't anywhere as hard as I feared. Main problems were:
Prob: Going through security with her in Ergo. Have to take her out and take ergo off and I can't hold her and put the Ergo back on.
Solution: kind man with kids at home held baby for 30 sec while I put on Ergo.
Prob: Plane lights strong and in babies eyes once she was asleep
Solution: None really. I don't use a nursing cover so i didn't have that option and all I could was try to position her better. Sitting in the bulkhead row with a baby bassinet was great except people kept walking across to get to the other aisle and many of them would bump the baby--one guy even used it as a handrail, twice! Grr....
Prob: Me needing to pee when she was asleep in the bassinet
Solution: Buddied up with the other single mom on the plane (with an 18mo old) and we tag teamed for potty breaks.
I had no hassles about having her in sling on the plane, but it was an international carrier. And like everyone said, nurse as much as you can!
Enjoy-I think a toddler will be much harder!
Carriers and security are 50/50. Ive been told I had to take her out at some places (Taiwan I think, Tokyo once, Chicago once, Rochester, Orlando and LAX) but was told I was ok other times (Orlando, LAX, San Diego, San Fransisco, Tokyo, Naha (also in Japan)). Ive found its better to just ask when you get up there then to take them out. Usually they want to feel between you and the baby to make sure you aren't "sneaking" anything in but it never bugged me since it was always a female doing it and if the baby was asleep they said never mind.
In the air Ive only flown once without a second seat. It was really hard but my daughter was 18 months old and the plane was overbooked. She was tired, I was tired, we were both crabby and running late SO it was just overall a bad flight. Luckily it was only 1 1/2 hours, if it had been one of the 11-12 hour flights Ive been on it would have been a pure disaster.