Hi A....Congratulations on your daughter and kudos for traveling with her. My son is 9 months and has already made trips to Chicago and Maui! First, it's a lot scarier thinking about it then doing it. There's a lot of great information here in the archives, plus all the great advice you'll get from your post. Here's some of my personal experience...
I dress my son in a sleep n'play outfit. It's got long sleeves and feet to keep him warm and protected. If you arrive late at night, you can put the baby straight to bed without worry. If you're arriving someplace warm, then pack a change of clothing for when you arrive at the airport. Also, always pack a backup change of clothing for both baby and you...you never know what might happen in flight.
We take a travel stroller (Combi) and check it at the gate. I also use my M1 baby carrier to tote my young man around. We park our car and take a shuttle, so this is a safe way to transport him. Also, you can take him through security in this without having to take him out. We throw the stroller on the x-ray belt and then use it to schlep the carry-on stuff through the airport. My son loves the carrier and it also relaxes him...he's actually fallen asleep in it while we were walking through the airport. In addition, it makes boarding the plane so much easier because you have two hands free.
We've never bought him a seat, just took him on as a lap child. The MOST IMPORTANT THING...nurse/bottle/pacifier on take-off and landing. Babies can't equalize their ears like adults can...this is the only way; otherwise they will have a pretty painful and noisy flight. On take-off, wait until you see the flight attendants sit down...if you start too soon, and there is a delay, then your baby may finish nursing before take-off. Also, keep it going until the pilot tells you they've reached cruising altitude. On descent, start as soon as you feel the plan begin downwards.
If you don't already have baby gear lined up at your destination, consider using a service like Baby's Away. We used them on both our trips and they were wonderful. We had full-size cribs, swings, and saucers delivered and setup before our arrival, then they pick them up at the end of the stay. They were delivered to both a relative's home and a rental condo. Great service!
There's lots more, but these are the highlights. Feel free to email me with any questions. Bon Voyage!