We're having the issue with our 20 month old right now. Fiber, fiber, fiber, fiber, fiber. It hasn't helped, though.
Certain foods are particularly high in fiber (such as prunes and pears). You can also get fiber supplements (we've been adding BeneFiber powder to her drinks the past few days).
I called the pediatrician, and they recommended Miralax. I chose not to go that way because of the cost vs. BeneFiber.
I had constipation issues last year when I was going through chemo. They recommended Senna-based products for both laxative and stool softening. They're vegetable based and were a Godsend. I called the pediatrician on that yesterday, and they said it was OK. The pharmacist wasn't sure what dose to recommend, but they did carry a liquid for $17.
Good luck. I'd see if you can get her to eat as many pears, oranges, etc. that have high fiber content and ask your pediatrician what they recommend as a stool softener.