A.V.
That's why I don't want to cut my DD's hair - I'm afraid her curls will disappear!
Anyway, my sister had really fine hair that wouldn't even take a PERM. I would do something other than curls. I would consider an updo, a fancy braid, some sort of hair accessory instead of just curls. While I did have much of my hair curled, I also had a twist around the top of my head which was very pretty.
How long is her hair? Could you do a waterfall or crown braid? http://www.brit.co/10-unconventional-ways-to-style-a-braid/