Don't fly at night. If she doesn't sleep, neither will you, but SHE can sleep the next day, and you can't! Also, if you're not getting her a seat, you won't be able to doze off even if she does (that goes for day flights, too).
We did the lap baby thing when DS was around...16 months, and I wouldn't do it again. It was convenient to be able to nurse him on takeoff, but other than that my arms were SO tired from holding him! DH's belly kept him from holding DS in those itty airplane seats, so it was almost all me, almost all the time. youch!
A year later we flew with him in a seat, and it was SO much better. He likes his seat, he could play with things in his lap, it was much better. Get her a seat if at all possible.
We didn't have a DVD player (portable) until recently, but I can absolutely see how it could be wonderful for a flight. I know that some airports now rent them!
On our way back last time it was just me and DS, and the flight attendant took a liking to him (and wanted to keep him quieter) and gave him a little packet of Southwest stuff...stick-on wings, crayons, a coloring book about SW. It was wonderful. I also brought stickers so he could put them all over his face (it's his hobby, I think)...cheap stickers that don't stick well, by the way.
have fun!