Can Being Awake Under Moonlight Inhibit Melatonin Production?

I normally go to bed at 1 am and wake up at 9 am. Sunrise is 6:30, so normally I only get 5.5 hours of sleep in darkness. Someone told me that sleeping in darkness is important because the body needs darkness to produce melatonin, which is important for good health. I sleep at 1am on weekdays because I work afternoon shifts during weekdays. I am now trying to make up for this by sleeping early during the weekends, e.g. going to bed at 9pm on Saturdays. However, I have noticed that if I go to bed at this time I often stay awake for a long time. What I want to know is if lying in bed awake produces melatonin or must I be asleep for melatonin to be produced. Also, I am slightly worried because moonlight comes into my room through the curtains and I am worried that moonlight might disrupt melatonin production. Should I be worried about moonlight?