A.J.
First of all just bring the carseat w/ you and either check it upon check in(it's not considered luggage so you shouldn't be charged for it) or at the gate. Most airlines will put in in a plastic sack and you can retrieve it when you get to your destination at baggage claim (it comes off w/ the luggage so be sure to watch for it). No she doesn't sit in the carseat onboard the flight...in fact most airlines don't allow that. If you bring a stroller it's almost the same deal...you can put it through the x-ray at security and check it at the gate...it'll be waiting for you as soon as you get off the plane, so look for it. So much easier going through the airport w/ one's child safely strapped into the stroller...and you can hang things (carry-ons) off the handles.
Snacks are a must...include something chewy so that your daughter can chew it on the ascent and descent, helps w/ the ears popping...I usually buy skittles for such a purpose but if you're adverse to giving her candy and chewy food will do (fruit snacks or dried fruit maybe). For the rest of the flight a nutritious snack that she likes...cheese, crackers, grapes...whatever. Try not to pack a drink because yes, sometimes that can be confiscated at security. Buy drinks after you've gone through security or simply wait until you're served them on the flight.
As for making your daughter more comfortable...a light blanket and a squishy pillow. Pack a backpack w/ those, her snack, and some entertainment...coloring books, regular books, electronic games (like a Leapster), animal figures (or whatever she likes to play with at home that's small and portable) pencils, crayons, blank pad of paper, magna-doodle. I have a mini-dvd player that my 8 year old son loves...but if you don't have that that's ok. Just bring enough to entertain her for a few hours. The plane ride alone will be exciting...looking out the window, getting served drinks, watching inflight movies (even w/out the sound), snacking on-board a plane (especially if she gets a treat she doesn't usually get). It'll all be new and exciting.
As for you and your comfort...a squishy pillow and light blanket would probably be good for you too! :) Have fun!