This was ingenious comedy. The old lady was actually a large knife, therefore she wasn't "fine" about going through the metal detector. But here are the underlying jokes.
When she said she was "fine", she indicated that she was "fine" as in "finely-sharpened"
Also, she was "fine" even though she was on the airplane and things wouldn't be "fine" based on the fact she could be a safety hazard.
Also, the knife indicated she was fine about not having any source of food.