Mine is 3 1/2 and is the same way. She was walking at 8 1/2 months, climbing out of crib at 14 mos, etc, etc. I put her in gymnastics, ice skating, etc. I started going to SKIP (for the mental stimulation for her) and we go to the pool once a week, and I jsut have to make sure that she gets physical activity every morning. If I don't, it's a mess. Sometimes, that is playing outside in the snow, sometimes it is the gymnastics, etc.
Then when my toddler takes a nap, it is quiet time, she can watch a movie (must be laying on the couch) or play quietly in her room, or something like that. I try to make it something with very little mental or physical stimulation.
Make sure they are eating good food (not prepackaged).
I have never had mine tested, but the fact is, she can play for a long time and be focused on her dolls, or other toys, without getting easily distracted.
Mine gets bored, and then gets hyper, so when she starts getting that way, I engage her in a craft or cooking or something that she can use her imagination with.
Good luck and hang in there, it's only because she is super smart.