I suspect she will be fine! They have a holding area for dogs going baggage/cargo but not sure as carry on. Unless you have a hard sided kennel with you, this might not be a good option. She can't stay in the soft unsupervised and you don't want her loose. That is one reason I really like the backpack Sherpa - it's easy to carry and no one knows there is a dog in there. I have gone into restaurants, bars, etc. no one notices. They think its a laptop case.
Happy trails.