Chess Prodigy?
Sounds like she's a really bright and good girl!
It is quite normal, that when kids at that age starts playing chess, they excel rather quickly. My experience is that they quite fast can match the level of other kids their age (that have started some years earlier), and if they are a bit talented and wants to work with chess, they can of course go further.
After just four months of chess, it is too soon to tell if your grand daugther is a chess prodigy or not. But my advise to you, would be to try to inspire her to join tournaments - both children tournaments and adult tournaments. At that age the quantity means a lot! And stop giving her a queen's odd - play normal chess with her, and play the best you can. She needs to learn how to lose as well, and it's the games you lose you learn the most from!