I know it's not the same exact thing, but I had to fly with my two toy poodles on a 6 hr flight.... If I would have left them for even a minute the whole plane would have had to listen to them houl and scream so I held it the entire time until we landed.... But I plan on flying with a 2 week old in the summer so if I really couldn't hold it I've thought of getting one of those carriers to put him on the front of me, but again I will probably just hold it.
I'm going to be traveling by air soon, also alone with my baby. I plan on wearing her. it won't be easy, but I don't feel comfortable having a steanger watch her. she has stranger anxiety anyway, so she wouldn't stand to be held by anyone else.
I've never had to fly alone with my son since my husband has been with me the whole time but I agree with baby wearing. Or ask a flight attendant to hold or watch your baby for a minute. They are more than willing to help. While I was waiting for my husband to get on the plane with our sons carseat a flight attendant held our son so I could get things in the overhead bins.