I read the Bell Jar in one sitting when I was 20. I felt down about it for the whole next day (sort of a minor feel-like-I've-been-hit feeling).

It deals very heavily with the heroine's suicidal musings and her various attempts at killing herself. She ends up in a mental hospital; here's a quote from the Wikipedia:

Originally Posted by Wikipedia
She receives electroconvulsive therapy, improperly administered, and feels she's being electrocuted like the Rosenbergs. When she tells her mother she refuses to go back, her mother smugly and callously announces, "I knew you'd decide to be all right.

Apart from the mental illness theme, she also considers her sexuality. Overall, I think the book is too mature for twelve-year-olds, but YMMV.

Here's a link to the Wikipedia article.

Val