Mydirtshovel, welcome and your daughter sounds delightful! You have correctly recognized that she loves learning but doesn't see any point in show-offing. So I would suggest to create an enriched environment for her to explore and learn at her own pace at this age. Apologize for the shameless plug, but I setup a montessori inspired homeschool room for my dd when she was about 3.5yo and she loves it. She spends many hours in it all be herself. Here is a link to the thread where I talk about all the materials in the homeschool.
http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/165584/1.html
