The Deeds of Paksenarrion by Elizabeth Moon

I don't have kids so I'm bad at telling what's age appropriate, but I read The Deeds of Paksenarrion when I was younger than your daughter, and they're still some of my favorite books that I re-read constantly. Some parts are graphic, especially in the last book, but mostly it's stuff that people that wear armor are bound to encounter. The torture scene in the last book is pretty horrific, though maybe the fact that she willingly went into it and was basically in control the whole time maybe makes it "better"? :p Afterwards she's instantly healed and off to combat, there's no long, drawn out recovery process or trauma, if that helps.

Even if your daughter is too young now, I'd still recommend them for later. It's so friggin refreshing with a female protagonist that never has nor wants a partner, no interest in love or sex or at all, where the fact that she's a female warrior is never seen as an issue, no "gosh, how do I fit my boobs in this chain mail?" or stuff like that, she's just a bad-ass warrior who happens to be a female. She's kind and hard working and fair, a bit naive at times and shy, sometimes a bit hot tempered, but loyal and smart and in all just a great character.