I think the quirkiness and the reluctance to "perform" on cue are both very age appropriate and very typical for little fifties. I would not ask her to read or show what she knows at this point, just let her learn and grow confident in her abilities. If you don't make a big deal out of stuff she can do, just show her you enjoy conversing about the moon phases with her as if it were the most natural thing in the world (and try to shield her from people who will either gush or be put off) she may grow into her abilities so that she'll enjoy testing even, because it is fun and challenging and she can have interesting conversations with the tester. Remember, she's very young!
I'd try to find out how far exactly testing dates for the schools you have in mind are into the future (with the option of early entrance, which I recommend) and then take a deep breath and let her grow.
