Hi C.,
I travelled to London with my 4 month old son alone, and then took 4 shorter flights within Europe so certainly have experience.
I bought him a seat on the long haul flight which was great but on a shorter one (less than 4 hours) I would probably have him sit on me. The airlines insist that even if you have bought a seat, the infant is on your lap during take-off and landing anyway. My pediatrician told me to nurse at those times, but having sat in the runway for hours, my son was asleep and the flight didn't bother him at all. If you tell the airlines in advance that you are travelling alone with an infant they will try to help you - they can offer you a seat at the front where they can set up a bassinet (free of charge). They may let you board the plane before everyone else too.
Also, carry as little as possible - I had a Snap and Go stroller and my baby's car seat as well as a diaper bag and my personal items (of which I had very few) but getting through security was a nightmare. No-one helped me at all - even when I was trying to collapse the stroller single handedly.
I have no qualms about flying with a baby - as long as you are prepared and are confident you can manage. Also, should your baby cry just remember that you will never see the people on the flight again! Actually, when my son fussed, many people tried to help out. They pulled faces at him and sang. One lady even tok him for a walk up and down the aisles. I wouldn't usually give him to a stranger, but a plane seemed like the one place he would be safe and he really enjoyed it.
Good Luck - if you need any other advice or think of something I forgot to mention, please feel free to e-mail me.
R.