I'm not too sure about anime that fit your description. But the first thing that comes to my mind for something serious involving rape is the manga Bitter Virgin.
Spoiler:
Niwa Daisuke is a very popular high-school student who could have any girl he wants. The only one he's not interested in is the pretty but odd Aikawa Hinako, who jumps like she'd been hit anytime a man even gets close to her. Through various circumstances, he ends up hiding in an abandoned church and hearing Hinako's confession:
In junior high, she was raped repeatedly by her stepfather, became pregnant and "had an abortion"(miscarriage). Her mother did nothing to help, so the abuse continued and she got pregnant again. This time the baby wasn't miscarried, and her body couldn't take an abortion, so she had to carry it to term even though in her situation it seemed less like a child than a parasitic thing growing in her. When the child was born, he was set up for adoption and she never even saw him. Despite how she'd never wanted to have him, or to see him, and had no idea where he was and how he was doing, she wanted to know if it was still alright for her to celebrate today, his first birthday.
At first Daisuke isn't even sure he believes the story, but gradually he becomes more and more concerned and involved with her, and finds himself falling in love with her, even though he knows there's no way he could possibly pursue any love there without hurting her even more.
Of recent anime with rape or something close, I can think of Okami-san, Fractale, and MM!, but Fractale is sci-fi, and Okami-san and MM! are mostly comedy.
And sorry if people aren't taking you seriously. It's not entirely easy to come up with something containing that sort of mature material that one feels comfortable suggesting to a 13-year-old girl. You might look on the site TVTropes.com under the trope "rape as drama".
One item that may work is Future Diary, which is coming out soon. It has some supernatural elements in the background, with a group of people fighting using "diaries" that show entries that they will enter in the future, but every one of the characters is messed up, and some have pasts involving rape or worse. Please note I haven't read the manga, so I can only go by what I saw on Wikipedia.