As cover357 said, going broody is a hormonal change in the hen. It has nothing to do with her age or whether or not you have a rooster.
To know if she is broody, you are going to have to observe her behavior both when she is in the nest and when she isn't.
When she is on the nest, does she have an almost zen-like trance look?
Does she flatten out when you approach the nest?
Does she also raise her hackles and try to appear larger than she is?
Is she staying in the nest more than out of the nest?
Has her voice changed to a loud bawk-bawk as opposed to her normal sounds?
Is she dropping a large smelly broody poo?
When she leaves the nest, does she eat and drink before returning?
Are the other hens giving her a rough time when she is off the nest?
If your're not going to hatch a clutch of chicks, it might be better to break her of her broodiness. IME, the longer she is broody without hatching a clutch, the longer it will take her to start laying eggs again. Being broody can be hard on a hen, and a good diet with extra calcium wouldn't hurt her.