Jim, it's much better to hit and lose one with an arrow than with a bullet. Arrow wounds, if not lethal, generally heal up cleanly with little or no trauma to the animal.
Dan Quillian had a theory that deer don't feel pain when arrow shot, and "proved" it by interviewing several hunters who had been shot by another hunter with an arrow. None of them felt the arrow other than a bump when it hit. Most said the first indication of a problem was when they felt the blood running.
She will be fine, and you may get another chance at her.