I took my 1 1/2 month old from Michigan to North Carolina to see her daddy off to Iraq and everything went fine! If you plan to fly with her stroller or carseat, I would DEFINITELY suggest checking the carseat! We have the carseat that clicks into the stroller, and on the way there, it was such a pain to have to gate check everything because you had to break it down, and you're rushing to get on and all that. The way back, we checked the carseat beforehand and just gate checked the stroller. I'm not sure how your baby will do on take-off and landing, but if she's fussy, I would suggest either nursing her or giving her a bottle. It kind of does the same thing as chewing gum for us. Something I didn't have, but wish I did was something to rest my arm on. I held my daughter the entire time, and something for her to kind of rest on (like a boppy maybe?) would have been nice. My daughter was overall a really good traveler, so I didn't have any problems. Some things you might need: diapers (just enough to get you by....you can always buy more down there!), wipes, pacifiers (extra ones in case they fall on the floor), blanket, bottles (if your nursing and worried about feeding, you can bring milk and a portable bottle warmer or ask the attendant for a cup of hot water), clothes, sleepers, socks, bath supplies (you can always buy those too....I just bought a little fold up bath "ramp" and took a bath with her), washcloths, and q-tips. That's about all I can think of right now. Good luck with your trip! It's definitely different when you fly with a baby!!
*By the way, it's ok for a baby to fly after they're 1 month old....they say the recycled air isn't good for babies younger than that though. I spoke to my doctor though and she said flying was fine!!