... to determine if they are really young enough to fly as no-charge lap babies. If the child is so young as to not be walking yet, they won't ask. (That is for domestic flights, of course. If you were flying internationally, she would need a passport.)
Give her a bottle (or nurse) during takeoff and landing; the swallowing will help clear her ears; if you go with a bottle, though, I'd suggest water. As this is your first flight with her, be prepared for the possibility of airsickness. Resign yourself to the understanding that an infant cannot use an airsickness bag; if she gets sick, you will be wearing it (and the person next to you might end up getting hit, too.) This means that you will need to carry a spare outfit for her, and one for yourself, too. I suggest unisex grownup clothing if at all possible; Dad could be holding her when it happened. Also pack several gallon-size ziplocs, a whole lot of wipes, and a small bottle of Febreze (your seatmates will thank you for that last one. A cloth diaper or two are helpful if you need to scrub at anything; wipes don't work well for that.)
Bring snacks and quiet toys, not for the flight, but for the wait in the terminal before the flight. Even though the flight is short, if there is a weather delay you could be trapped in the terminal or on the runway for several hours; be prepared for that possibility. Gate check your stroller (remove all the loose accessories from it, first, though, and fold and secure it yourself at the end of the jetway.)
I know that this makes it sound like you are preparing for a battle campaign, but it isn't, really. Being prepared for the worst doesn't mean that it will happen, but if it does happen, you'll be able to clear the hurdle without breathing hard. Take it from me, the woman who once got off a 45-min. flight from Atlanta wearing a flight attendant's pajamas. (We had been stuck on the runway for 3 hrs before takeoff, and the plane's AC didn't work on the ground. My son did not react well to the heat, and the worst happened, about an hour into the wait. He drenched me down to my underwear, and I would have had to stay that way for the next 3 hours, but an FA had pity on me and gave me her pajamas. That woman has been assured a place in heaven.)