Erik7181,
I strongly recommend that you call the airline and find out the exact dimensions of the space under the seat in front of you for the aircraft you will be flying on. I recently did a lot of research for a 1st flight with Pritti and found out that in almost every case, the most common of the small pet carriers is too tall for the under-seat storage, but one to two inches. To avoid any problems for going and returning home, you should call airline and ask hem to look up the exact aircraft of your flights -and- for back-up you can google the make / model of the aircraft and find out yourself (i.e. Airbus #ABC123). The generic seat heights listed all over the internet do not apply in many planes.
Also, I found an excellent transport cage if you find that you will need another one. It is very roomy inside, but is only like about 9" tall (see this thread for a photo
http://www.parrotforums.com/conures/21521-flying-airplane-bird.html) and about $30 delivered. Pritti is about 14" long and seemed comfortable sitting on the little perch I connected inside, towel on bottom so he wouldn't slide around. Fold small towel in half, so you can then reuse the other side when it gets soiled. Bring an extra one. I kept the top covered up on and off when there was a lot going on so he's be relaxes.
Some say to not feed them for 2 hours before so that they don't make a mess and don't get stomach sick - I have to admit that I fed him treats rather often by sticking my hand inside the little trap door on this cage (chopped apples, popcorn, and a few almond pieces). I also put water and food dishes in as soon as I boarded.
If you are taking a connecting flight, be sure to ask about the under-seat dimensions on the second flight. One of my options had a MUCH smaller size on the connection and NO WAY the regular small kennel would have fit -- then what, I wonder. I wound up on a direct flight and everything was fine. But I will say that in Florida heading out, security was a small fiasco, so leave extra time in case.
Have a great trip. Your bird should be happy to get in to the nice subtropical climate right about November.