I am a hairstylist, and yes it sounds as though the ponytails are causing the breakage.
I would advise you to do more braids, maybe even clip the hair in the front in a cute little barrette, or two barrate on wither side of the head (think around the midpoint of the eyebrows), and then braid it all together down the back, nice and simple, especially if you are not great at french braiding.
Another option is to do a lot of little twists and pin them together. Or try twistring it in a little ballerina bun would be cute. Just try to keep the tension even throughout the hair and to not put all the pressure on the same spot every day.
Also, avoid putting her hair up when it is wet or damp (of course, in order to braid, you will need to spray it a bit with a water bottle in order to hold it well).
You can always try deep conditioning treatments, but those typically work best for chemical damage, not mechanical damage like breakage.
Here are some good resources to help with your styling options:
http://www.expertvillage.com/interviews/hair-styles-young...
The "twisted butterfly" on this site is super easy and cute:
http://ok.essortment.com/hairgirls_rnhr.htm
http://www.expertvillage.com/videos/hair-styles-young-gir...