I do stuff when I can't sleep. Well, stuff that won't wake anyone up that is.
I have a friend that painted most of the rooms in his house between the hours of 11pm and 5 am. It really is amazing what you can do when there's no one around/awake to bug you.
If you're like me your schedule is just shifted back a few hours. Having to get up at 5 am to really do something like work or what not will generally shift you back, just don't take any naps no matter how tired you are. Seeing a doctor might help too but he's likely going to put you on sleep meds. Then zombie time.