I have to 2nd that being scared, sad, happy, etc., is desirable in reading... (*I* cry during sad parts!!)... it's the line though that we walk between feeling emotions and being overwhelmed by them. So when you say cry, I'm assuming you don't mean bawled for hours, inconsolable, with nightmares for weeks. Crying = healthy, losing it = "okay, we'll wait a bit on this one".
For my son, Disney cartoons were terrifying for him as a toddler... but StarWars, Indian Jones, Pirates of the Carribean, & Harry Potter weren't. One of the things that's nice about HP is that JKR originally wrote them for her kids. So they get increasingly more mature as you read them. The first book is VERY childlike, and then each book gets a little "older". The first 3 my son loved, book 4 started getting scary, so we held off a year and a half, and we're just about to do book 5 after waiting another yearish on that one.
It's a bizarre thing with children's lit. Many of the themes (from the boxcar children being orphans -FREAKED my son out, to Matilda and her evil uncaring parents, to Charlie & the Chocolate Factory, to x, y, z) are just really, really out there. Sometimes kids handle them with aplomb, sometimes they are just too much. I know my kiddo handled "adult" things better than "children's" things for YEARS... because adult things have subtly, very rarely is it GOOD against EVIL, like you find in children's thing. I mean really... Snow White's mum first wanted her dead in the woods, and then poisoned her... the death of the loving mum to the evil step sisters and slavery in Cinderella... being turned into a helpless shriveled thing in Little Mermaid... Stephan King could have a field day with these themes.
So I would say... try it and see. If she loves it, she loves it. If not... it can live on the shelf for a few years.