how wonderful to begin taking your little on one plane trips now!
if you purchase a seat for her, you may use your car seat just as you would in the car (some airlines offer discounted seats for children under age two). if she is going to be in one of your laps for the trip, then i would suggest doing a gate check on your car seat. this allows you to carry it all the way to the door of the plane. you hand it to a flight attendant and they stow it under the plane for you. when the plane arrives at your destination, you will find your car seat (or stroller if you do this with your stroller) waiting for you at the door of the plane when you exit. do be sure to label both the car seat and the base (if you're not checking the base).
with regards to formula/snacks, etc. for your little one, you are allowed to bring "a reasonable amount". in most cases, you are not allowed to bring your own bottles of water past security (they are too large) but you can purchase bottles of water once you pass the screening area.
the best thing to do is to check the TSA website for up to date info/rules: http://www.tsa.gov/travelers/airtravel/children/index.shtm
it is TSA, not the airlines, that makes and enforces the rules regarding certain substances. some airlines may have their own guidelines, but ultimately, you will want to adhere to what TSA (federal) requires or you may not make it to you gate with everything you wish to carry on.
as far as tips, the best one i got (and it works!) is to be sure your child is drinking/sucking or otherwise swallowing on actual take off and landing. this helps with the pressure in their ears (they can't exactly chew gum yet).
i hope this helps you. have a wonderful trip!