I agree. I would keep her with the group of little ones and eventually she'll start to wander and find her own fun. I assume that there are no other children her age there. This can be tough as children of that age begin to play really well with other children and crave companionship. There's nothing you can really do about that unless you take on another child.
I might use the special one on one time as a treat (bribe). If she is able to complete X amount of activities on her own then you have a special project for the two of you to do.
Love the idea of a challenge=reward for her to be more independant.
Children are great imitators.
So give them something great to imitate.
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