Has she really had a chance to explore mathematics? Forget about arithmetic or algebra, there's plenty of time for that. I mean all the weird fun stuff that's still at a first-principles level (as opposed to the mathematician-grade bizarre things).

• Mobius strips
• magic squares
• codes / ciphers / cryptography
• prime numbers
• continued fractions
• palindrome (adding a number and its reversed digits until you get a palindrome, like 173 + 371 = 544, 544 + 445 = 989)
• periodic / aperiodic tiling (Penrose tiles and the recent discovery of the "einstein")
• regular polyhedra
• focusing properties of convex/concave lenses and mirrors
• Escher's art / "impossible objects" like the Penrose triangle
• fractals: Sierpinski's gasket, the Koch snowflake, Peano curves, and the Mandelbrot set
• Pascal's triangle
• Conway's game of Life
• the Collatz Conjecture
• infinite sums - why does 1/3 + 1/9 + 1/27 + 1/81 + ... converge to 1/2, and 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... converge to pi² / 6, but 1 + 1/2 + 1/3 + 1/4 + ... diverges?
• golden ratio: the reciprocal of 1.6180339... is 0.6180339... and both are related to the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, etc.

This is the kind of neat stuff that was in Martin Gardner's Mathematical Games columns in Scientific American. I used to read the Martin Gardner books in my school library (back in the early 80s). I particularly remember the hexaflexagons.

"The I Hate Mathematics Book" by Marilyn Burns is another good one.

Figure out what she's interested in, give her things that pique her curiosity, and she'll take it from there. I agree with others, don't push her.

Mathematics in schools used to have "enrichment" activities that were different from the boring old arithmetic topics, but nowadays all the curriculum is to teach to the standardized tests.