I traveled from Connecticut to Cyprus with cat (3 flights) and she was with me in the cabin the entire trip. I recommend a soft sided carrier - it's easier to fit under the seat in front of you. I lined my cat's carrier with puppy papers in case of any accidents but she was fine the entire trip. My Vet advised no food or water starting 4 hours before departing for the airport. The carrier had to be under the seat for takeoff and landing but during the flight I had the carrier on my lap or the empty seat next to me and I was able to unzip the carrier a bit to put my hand in and pet the cat to assure her that I was there and she was ok.

You will need to check with the airline before you buy your ticket to make sure that they will allow an in-cabin pet on the flight you want.