Good advice, and I wish Nan's warning wasn't nescessary, but it is.
So having lists of books and some Math worksheets filled out in the child's own handwriting is very important, but perhaps even better is to have a video that you can show of your child talking about some of the more advanced books and talking about how a person can figure out the Math that she did.
Perhaps you can approach it as 'playing school' showing how she would teach someone to do the Math, and 'making a commercial' for her favorite books like in the TV show 'Reading Rainbow.' If she has a favorite topic, such as weather, also have a clip of her talking about that. Even if the school doesn't believe their eyes, you will at least have the Davidson YSP application halfway complete. Even if you have a phone that takes video, showing her in action is better than only showing hard evidence.
Remember that elementary schools are trained to believe that abstract thinking is 'impossible' in children and therefore 'not in their job description' to develop, so keep talking their language and consentrate on what skills she has.
Best Wishes,
Grinity