Sounds like the others aren't picking on her. Is she crested?
Seems like if something was prowling around or some other type of disturbance the others would be up and moving around also.
No she couldn't be broody, What are you feeding them? Do they have access to feed and water 24/7 at a month old they need feed and water 24/7 until around 6 weeks old then they can go over night with out both. Is her weight the same as the others. And have you noticed any other symptoms besides...