When off the nest, is she making a low, constant 'book-book-book' sound? Walking around with her feathers fluffed? Glaring, screeching, or acting threateningly toward the others if they come close? Defending her nest by growling, screeching, or pecking your hand? I have hens that spend hours on the nest while deciding if they're going to lay or not and they never go broody, but if she wanted to sleep on the nest, that sounds more like broody behavior. However, keep a close eye on her just in case. If she's not exhibiting much as far as broody behavior and just wants to sit on the nest, she may be ill and wanting to seclude herself in a dark place to rest.
As for what to do with her if she really is broody, it depends on whether you want her to raise chicks or not. If you want her to brood, leave her be and see if you can find some fertile eggs for her. She's awfully young and may not stick with it for long, though, so I wouldn't go too expensive on hatching eggs in case she quits on them.
If you don't want her to brood, keep her off the nest as much as possible. Some say if you leave them be they'll snap out of it after the amount of time it would have taken for eggs to hatch--however, I have heard of hens brooding for months and months and becoming dangerously thin. When my girls start to brood, I get a piece of fence, a dog crate, or a cage of any sort, just something to keep her off the nest but still in the flock, and keep her there until she quits. It usually doesn't take long, especially if she's in a high-traffic area and has nowhere dark or hidden to go to to keep her brain on brooding. Most of mine quit within a week or two of being kept off the nest.