I fly with Sadie twice a year on Southwest. They are very welcoming to her and I must say she is a saint. Some folks won't sit in my row if they know she's there, but she never makes a peep.
I do not feed her before the flight and take a pee pad, wet wipes, and a small plastic bag, but she has never needed them. The ladies in the bathroom are always good about my putting a pee pad down, but has never used it. She just loves up the ladies!
I swear, God gave me the best puppy in the world.