If anything, OVER CURL. Since your daughter has straight hair, really tight curls will take longer to fall out. They'll eventually fall into looser ones as well.
Also, have you ever tried sleeping in curlers? I had to do it for school cheer and they would not budge. There's a product called Curl Booster (in a yellow bottle with purple lettering) that you can try. Take the piece that you are going to put in the curler, spray, roll, spray again. Spray the whole head once you are done. Sleep on it then wake up the next day and spray again.. but leave about 1-2 hours before you actually remove the curlers. After then I would recommend using hairspray.