I'll break this response up into two parts:
- What you should say to your niece, and
- Why you should or shouldn't let her watch the show.
Do forgive me for plastering the word "cartoon" here; my gut feeling tells me that this is the animation age ghetto which Anime just loves to be pigeonholed into.
Not all cartoons are meant for children. There are some which are meant for a more mature audience, like teenagers or adults. In this specific show, the characters deal with harsher and more serious topics than you've ever watched in a normal show; this is something that I'm not sure you'd be able to handle at your age.
It's not only important to look at the cover of the show to give you a rough idea of what it's about, but also its age rating. The rating says it's 13+ because of the things it discusses: violence, horror, and a lot of psychological ramifications of being a magical girl.
Even after what I've said, if you're still interested in seeing it, let your parents watch a few episodes first. Make sure they give you the OK before you watch it.
Just so you understand, this isn't the same type of cartoon you're accustomed to watching, and you may have a lot of concerns, confusions, or fears from watching it. If you want to talk about it or ask questions, I'd be happy to answer them for you.
So, should you let your niece watch it?
Well, it isn't your call. It's her parents' call.
In the response above, I ensured that the responsibility of making that judgment call was given to her parents and not you, since you don't want to be on the hook for introducing your niece to something she might not have permission to see. That said, so long as said permission is obtained, there's no further objection on that front.
In my opinion, she might actually like the show. She's at an age at which a deconstruction of a work she's familiar with may give her a new perspective on the genre as a whole, which could serve to mature her and frame her opinion on anime and manga altogether in a way that isn't terribly one-dimensional. You also have to balance this with the possibility that she never trusts a label that has colorful pictures and magical girls on it ever again.
It's important that you treat this as a recommendation you'd be making to a friend. It's just that the "friend" you're recommending this to would be your niece's parents. The niece has to understand that this isn't something you can simply cosign on and say it's okay to watch, and the parents have to understand what it is they'd be getting their daughter into.