Just try some of the dietary modifications as you cant give her medications for long time.
give her fiber rich diet like boiled vegetables ex-carrot,cauliflower,etc
give her green leafy vegetable soup ex-Spinach
as she can chew give her fresh fruits daily cut into small pieces.
try feeding different foods daily as this will not make child bored of same taste.
give her enough fresh fruit juices and water
If you try these modificatios in her diet definitly her problem of constipation
will be cured and will never return
Hope i have tried to anwer your query.