Take the small juice boxes - they are expensive but they are acceptable. Then you can toss them as they are used. Take snacks in baggies so they can be compressed or tossed as things are eaten.
Take a bunch of new, small travel games/toys - things that are quiet to play with but will be BRAND NEW to her. Play Dough is okay (take a sheet of wax paper for the tray table if you want to), Duplos can work if you have the space. Get some books from the library so you don't have to pay for those, or go to a children's resale shop, or get something on your Kindle if you have one. Set aside some for the terminal itself, others for the plane. Only show her one at a time - don't let her see that there is a treasure chest!
I've seen some people make up goody bags for those in adjacent seats - the 3 in front, the 3 in back, and the 3 across the aisle. They put in all kinds of stuff, like disposable ear plugs, a package of crackers, and some hard candies and so on, with a note that says "we are traveling with a toddler and hope things go well but we also hope you have a good flight". Usually they use a clear plastic bag tied with a piece of curly ribbon with the note attached. Since parents pre-board, you can leave these bags on the seats before the other passengers board. Seems like a lot of effort but it can smooth the way with cranky adults!
Since you will board early, you will be guaranteed overhead storage by your seats, so everything will be close by. I have mixed feelings about bulkhead seating vs. regular. Bulkhead gives you more leg room but no space under the seats ahead of you for your things. And I think the tray table is good for toddlers and children.
The agents are usually good with kids - they are used to it especially as summer approaches (and they've just been through spring vacations).
The car seat is ideal on the plane because the child is already used to it in the car, and then you have it on the other end. You can gate-check a stroller (regular or umbrella) and you can just put your carseat and bags on the rental luggage cart if you need to, unless you can strap the carseat to a larger bag (probably cumbersome but it will get you to baggage check if they don't have it curbside).