There are a couple of other messages from me because for some reason my comments don't show sometimes-so lucky I've learnt to copy them before submitting!We do 24 hour flights regularly with our sons, icluding the first time when he was also 19 months. The worst part of the flight was that he got overtired and started screaming-so watch that she's not missing her bedtime. Also don't forget either her bottle or some chewy sweets to release pressure built up in her ears-its very painful and many parents are not even aware of it!I keep some chewing gum in the flight bag permanently these days in case I forget.its only during take off and landing that you need to worry,until the seatbelt light comes off is my rule. Get some of those inflatable neck support cushions-they let you sleep sitting upright. I usually put my oldest (now 3)by the window and put two pillows (or a balled up blanket)on the window's armrest,she will snuggle down easiy and put her head on it. Another option is raising the armrests and letting her put her head on your lap. The airlines are usually very helpful when they see you travelling alone with her-you should get the bassinet seats (leg room/toy room) or they would put you next to any empty seat if available. Don't make the same mistake I made - I took too many bags and had to carry them on my own-very tiring when you have a little one. Ask them to let you take your own stroller on the plane,say that you are travelling alone and will need it. Usually this works and they put it behind the last business class seats-if not you can ask them to have it ready when you get off the plane. If they still won't help not only will you not be flying with them again-you will have very sore shoulders from carrying the baby and or the bags. Also try to get a child restraining lead in case you don't have the stroller at all times. Also take a little first aid kit on the plane with infant paracetomol (give this before you board regardless),some homeopathathic kids calm remedy,a thermometer, and anything else you may need. Also don't forget plastic bags to put dirty clothes in. Make sure you have enough diapers (I had to buy a bag of 30 in singapore airport because I had accidently put the diapers in the wrong bag). Good luck and enjoy your flight! :)

G'day,
An idea I have is to use one of those pocket seats. It would be fastened or pulled down over the top of the plane seat. It might work for those times when you need her a little more restrained. Here are a few links to the different ones I have found.
www.totseat.com/
www.yourbaby.co.nz/

This one is more of a traveling site for kids. I think it might be useful for you.
www.babygoes2.com/main_equip_onmove.asp

Forgot to mention-hehe this was the whole point- I just use the seatbelt on the plane but turn it inside out so it can't be opened by her. Sit her on your lap during takeoff and landing-its the only way!

As difficult as this sounds, the really only thing you can do is keep her distracted...  Take an activity bag of sorts, things she likes. I am not sure what airline you are flying but if you are lucky enough to get one with her own little screen you have a winner there... (well unless your child is like mine and only sits through half a movie) still it is better then not sitting at all. 

A girl is a little different to a boy I am guessing unless she loves cars. I was lucky enough to be able to take my sons cars and he played for hours just smashing them together saying Vroom vroom...   Thankfully he did not get board with those..

Good luck...