We recently flew with our DD, although she was 2, not 3. A few things I learned.
--I understand the debate about car seats on planes, but my DD would never sit in it. She hates her car seat and would scream the whole time. We bought her a seat, buckled her in, and sat her between my DH and myself so she couldn't get out. She also spent time nursing, just sitting on our laps, and sleeping. You would also have to haul the seat all through the airport, and that would be an enormous PITA.
--You might consider checking your car seat, though. We were supposed to rent one from the rental car company, but when we got there, they were out. Fortunately, we were visiting friends, so they loaned us one of theirs, but otherwise, we would've been without a car seat in the rental car. Maybe if you call ahead directly to the local branch, instead of the 800 number, you can speak directly to the manager and VERIFY that you will have a car seat waiting for you.
--The biggest hits for my DD on the plane were stickers and food. A 3 year old might enjoy books and coloring more than she did, though.
--Definitely wait as long as you possibly can to board. It's much easier to entertain a toddler in the airport than on the actual plane.
--I have friends who swear by walking with their toddler walk up and down the aisle, when the flight attendants aren't pushing their carts, but we never had to.
--Check as much as you possibly can, so that you carry as little as possible through the airport. The only things we brought on the plane with us were our diaper bag and a duffle bag with toys, snacks, extra diapers, etc. The baggage claim area is usually right near the rental counters and shuttle buses, but you may have to walk a LONG way to get to that area.
--In the airport, we had a little bit of trouble with our DD not wanting to hold our hands but also not wanting to be carried. She kept wanting to run ahead. We found a great trick, though. DH would take one of her hands, I would take another, and every few steps, we would pick her up and swing her and say, "Wheeeee." We made it through huge stretches of airport quickly and easily by doing this b/c she wanted to hold our hands the whole time. Again, though, it was possibly b/c we only carried one small carry-on bag each. It wouldn't have been possible if we were schlepping a lot of luggage or a car seat.
--We borrowed our friend's umbrella stroller, but I almost wish we had checked our stroller and brought it instead. It is more comfortable for our DD and has storage room underneath. However, if you're going to DW, you can rent strollers there. They don't recommend taking your own stroller b/c you can't take it on a ride, and stroller theft is rampant. It might be handy to have your stroller if you're doing local, non-DW sightseeing, but if you're doing only DW, I would just rent one there.