I think it is a personality thing. Some kids do it for a long time, others don't. That main thing that strikes me from your post is that she does not want to be alone in her play room. My son would and still will occupy himself for a long time, but usually preferred to be in eyeshot of me at age 2 and to some degree still does. So playing by himself was fine, being alone was trickier. Perhaps if she could bring a few toys out to the living area and play were you are still in earshot? I love out open floor-plan hose for this reason...Toby can play to his heart's content in the living room and still know that I am right there in the kitchen or dining room since he can see me.
Katie, mama to a pair of boys.