I was going to suggest Higurashi but that's one of the top suggestions from everybody. You might check out Bakemonogatari. Also Venus Versus Virus, Dance in the Vampire Bund, Mirai Nikki, Sankarea, Shakugan no Shana.
About the age thing, my cousin is 11 and she has seen most of the anime I've seen including Yosuga no Sora for example which surprised me when I first started talking to her recently, but that's not really unexpected these days.
I didn't care for the main male character in Mirai Nikki but I watched it for the yandere experience anyway. I have no opinion on the manga but I never really got into the manga format. I like reading regular books though. If it's more of a novel than I can get into it easier, I read the Death Note BB murder case awhile back for example.
I personally enjoy the psychological-type anime myself, although most of the series I've seen have been more thriller or drama than horror (I don't mind horror I just haven't seen a lot) and I really enjoyed the anime you mention. I would recommend monster. It's a slow burner (74 episodes) but it's a really good series and one of my personal favourites. Some other series I'd suggest would be serial experiments lain, psycho-pass, texhnolyze, rahxephon, ergo proxy, steins;gate, phantom requiem for the phantom and neon genesis evangelion among others. That should tick your box relating to psychological but not for horror unfortunately. I hope you enjoy some of the series if you get round to watching them
About the age thing, my cousin is 11 and she has seen most of the anime I've seen including Yosuga no Sora for example which surprised me when I first started talking to her recently, but that's not really unexpected these days.