Is it a good idea to expose a 9 year old to anything related to medical science?

Why not? It's good that she develops an interest early on, and she's lucky that you allow her to. I know people who forbade their children such things, and the children grew up to be scared of the thought of blood or an operation. Just make sure that she also knows that, even if Discovery Health usually shows the good side, there's a bad side as well, and that mistakes are very costly and possibly fatal.