ETA: Dress comfortably. Do NOT wear boots, etc. if you have a heavy jacket? leave it at home - if you can check the weather in Florida prior to leaving - I would - you may be carrying stuff you don't need. Do NOT wear complicated shoes. When I went to Austin in December - I wore my slip on shoes. Easy-peasy.
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You have never flown on a plane before?! WOW!!! How exciting!!
Are you flying out of Newark or JFK?
Depends on where you are flying to - you say the flight is 2 hours - so I will assume it is a U.S. flight? Not international? If it's international - 2 hours is plenty of time to clear security - passport checked, etc.
I would arrive 1.5 hours prior to departure time.
I would have my carry on ready to go through security - no shampoo, hairspray, knives, etc. you can go to TSA.gov to see what is acceptable to bring abroad - the 3 - 1 - 1 rule I believe is still in affect - no more than 3 ounces, 1packages (1 quart ziploc bag), 1 bag per traveler.
Southwest is what many call a "cattle call" - there are NO assigned seats. When you check in you get a Letter and a number - A10 or B or C or D. The later the alpha - the later you board.
If you want to have your shampoo, etc. with you? put it in a large ziploc bag and put in your checked luggage. Same with perfume.
You can have food - but no drinks - any drinks you purchase BEFORE you go through security will HAVE to be discarded. You can ONLY purchase from vendors once you have passed security.
Have your ticket ready along with a photo ID for you and your kids. We used the Ident-a-Kid ID and the security crew loved it. Made the kids feel great too!!
http://www.tsa.gov - this will give you all of the rules for travel.
I wouldn't take ANYTHING to sleep through a 2 hour flight - that is me. If you have ear problems - check with your ENT prior to your flying. I use Advil Sinus congestion to help with ear pressure. Chew gum. That helps as well.
RELAX!! ENJOY THE FLIGHT!!!