There's a movie with Dr. Tim Noakes, The Magic Pill, where exactly that happens. The little girl is 3-5; it's hard to tell because she acts uncontrolled like a toddler, and will eat only three junky things.

Over the course of the documentary, they transition her to low carb. And she is transformed into a verbal, happy, little girl who seems to have developed a couple of years in her skills.