When I was little (in the prehistoric era:) ) my mom gave me a book around 6 mos before I started around 11 as well. I was the only girl in my catholic school class of 30 to have a period for 2 years... and to have a divorced mom and to be a little overweight:)
It helped to know I wasn't alone, I wasn't "the only one" and I wasn't "weird or abnormal". I was an only child living outside a neighborhood, so that "alone" feeling was very real for me, and perhaps magnified for your daughter as she is now "unlike" her beloved sister in one way.
Girls and women are emotional as well as hormonal, and she should be allowed her feelings as long as she's healthy in their release:)
Try getting her a book or surfing online with her about all kinds of kids and cultures and advice that's now available and we didn't have:) I'm sure there's more out there, but here's what I am bookmarking...
"The Period Book: Everything You Don't Want to Ask (But Need to Know)"