Oh I remember all too well wanting to "be" a classmate of mine, in about the second grade...she had long, thick, dark braids (my hair was stringy and pale) and she had a "cool" mom who wore fashionable career clothes (my mom was stay-at-home, which in her case meant she stayed home all day watching soaps and smoking virginia slims.) I don't know if it's "normal" or not, but I think most girls, at one age or another, long for someone else's life...maybe some women do too :)
But I know how you feel. My husband is dark, and I am white as can be, blonde hair, freckles & blue eyes. My daughters have GORGEOUS brown skin and deep amber brown eyes, and guess what? They both, between the ages of 4 and about 10 or so wished they could be blonde! I don't know if it's a cultural or media thing, but as a previous poster said, just keep pointing out to your daughter what makes HER special. In my case, when I shop with my girls I'm quick to point out all the cute colorful clothes that look so nice on tan skin.
Hang in there!