It's possible that she is needing more exercise. Do you walk her regularly? If she's left home for several hours during the day, she needs an outlet that's more than just playing in an area of your home. Also, the fact that you're playing with her at 3am is reinforcing her behavior to get a desired response from you. Is it possible to have a dog walker or doggie daycare a few times a week? I can be pretty sure that if she's getting tired enough, she will sleep at night. Good luck, and remember, she's still just a baby.
