So glad to hear that it all worked out!
I know it's hard, but you have to keep in mind that the transplant team could find some reason that you should not be a donor at any time, even the day before. Or they could find some reason that your cousin isn't stable enough to have surgery on the given day. (That was the most stressful part for me. They had a really hard time getting my recipient's hemoglobin up to an acceptable level and keeping it there.) Try not to freak out, and best of luck to you and your cousin!
Morgan