Also not princess-y, but I loved the mystery series Encyclopedia Brown when I was a young child.
It's kid-based mystery, so no one dies (or ever even comes close). Even the usual bad guy/bully does little more than bluster and always gets his comeuppance thanks to EB's intelligence and cool head.
I'd second Grin's Little House suggestion, though IMHO, you probably need to have a talk about the treatment of Native Americans in the books along the way. The attitude of the series is *ahem* not very enlightened *ahem*.
