Do have a lot of snacks available
Don't have them in your backpack under the seat in front of you. With a child on your lap, bending over at the waist and actually breathing can be somewhat difficult.
Do bring a portable DVD player
Don't forget to charge it, and try not to fly for 3 hours and 45 minutes straight! Don't forget to bring movies that your child actually watches, and don't forget headphones (because hearing is near nil capacity at 30,000 feet) also good to make sure the said child would actually wear headphones!!
Do wear sweat pants or something stretchy
Don't try to be chic on a flight with a child. It is uncomfortable and something may rip. If and when your child does fall asleep, she cares not that her drool (and/or snot) is all over your outfit when she wakes up!
Do bring water
Don't let your child (or the flight attendant for that matter) convince you that she needs coke to drink on a 3 hour and 45 minute flight! It causes many problems; bathroom visits and incapability of holding still on mothers lap are the most common!
Do bring books, coloring tools and lots of paper!
Don't carry black sharpie in your purse though, passenger sitting next to you can be somewhat grumpy at end of flight!