I agree with Heather. Take easy to eat snacks in ziplock bags. Gold fish, animal crackers, fruit snacks, anything that she loves, maybe even an item or two she doesn't get very often so it is special. As for a drink, you'll probably have to wait and purchase something after you've gone through security. In August I flew with my 5 month old son and 3 year old daughter and they made me pour out all the water in sippy cups and bottles. I then had to pay a premium for water inside the airport.
My suggestion is to take a back pack instead of a standard diaper bag. This will allow you to have it on and have both hands totally free. I didn't take my purse, I used one compartment of the backpack for my "purse" and put my wallet, sunglasses and other necessary items in there.
Take something to entertain her with. A portable DVD, colors and a coloring book, a favorite doll. We bought new colors and a new coloring book and I joined in the coloring fun. My daughter actually enjoyed looking out the window almost the entire flight.
Take a stroller. You don't want to have to chase your 2 year old through the airport. The stroller can go all the way to the entrance of the plane with you, make sure to tag it with your name. Then when you get off the plane it will be waiting there for you, or you may have to wait a minute for it.
You will want to make sure the rental car company has a car seat reserved with your car as they don't always have one availble. It would be horrible to get there and not have a car seat. If you have to take yours, check it in with your luggage. The airport has large, thick plastic bags to put them in. I had to take two with me. I had a little wheeled cart I bought at Target or Walmart (don't remember) and I bought some bungy cords and attached the car seats to the cart so I wouldn't have to carry them. If somebody is taking you to the airport, do the curbside check-in for your bags, that way you don't have to go far.
As last, don't worry about other people. That will add to your stress and likely add to your daughter's as well. I've learned that most people are sympathetic, but there are those that can be rude - they are usually people that have no kids of their own.
Get to the airport early. That will leave plenty of time to purchase some drinks (make sure you have an empty sippy cup in the backpack), give you time for the restroom before you board and things of that nature. Most airlines allow you to board first if you are traveling with a child, I would make sure the counter at the gate knows you are alone and pregnant with a child. Depending on the airline, they should be very helpful.
Good luck and enjoy your trip.