Questions:
Why does her family want the world to be in darkness and chaos? This is probably one of the most important aspects. The 'generally evil' people tend to make stories silly and unbelievable. If you give them a good reason to want this, then I think the whole story could work.

Why does the girl not want to help her family? If she grew up with them and being taught by them, what makes her think that anything is wrong with this darkness/chaos they want?

How do the townspeople find out her destiny? Is this like fullfilling a prophecy or does the girl just tell her name to everyone or what?

What kind of demon are we talking about here? Christian/Western demons or Eastern? If Eastern than this makes sense to me. If we're talking Christian/Western, why does the demon have the power of Light?

You might also consider playing with a concept other than Light and Shadow. Using these terms make it sound a bit... simple for the concept you're trying to play with.

Overall, I think the story could work! I say go for it.