I recently traveled alone from Florida to Oregon with my 2 1/2 year old and my 6 month old. It was tricky, but not as horrible as I thought it would be. In fact, the toddler was easier to travel with than the baby. I packed a backpack FULL of toys, activity books and snacks that she doesn't normally get. Sticker books, coloring books (with washable crayons), those "magic" crayola markers that only write on special paper, colorforms, little trucks, a box of Dora dominoes (suprisingly, these kept her occupied for a looong time). When we changed planes, I let her run around a little bit and then she actually slept curled up in her seat for over an hour.
You will be allowed to bring liquids for your child--I brought a small juice box and a sippy cup with no problem through security.
My other advice is: wear slip-on shoes so you can get them on and off easily at security, go to the bathroom right before you get on the plane (don't think you're going to be able to do it on the plane!), and never feed your child a blueberry muffin before a 4 1/2 hour flight (side note: birng lots of wipes).
Good luck!
--E.