Our Royal's first eggs were laid when she was six months (Dec.) old. Both she and the slate hen were pretty spotty with the egg laying until May. They would start a nest and lay eggs but return to the shed in the evenings. Once they had what they considered to be an acceptable number of eggs in the clutch they would go broody. Set up some nesting boxes but, be aware, the turkey hens can get pretty adamant about where they want to nest (need lots of redirection sometimes - lock `em up where you want them to nest).
You'll know when they're getting into the `mode' when you hear them making plaintive `whoot', `whoot', `whoot' calls and walking off into the woods paying a lot of attention to cozy bramble overhangs - off to lay an egg (track `em down, grab the egg(s), place `em in nest box in secure pen). Once they go broody they'll usually only leave the nest once every few days to eat/drink dirt bathe/ poop.
Oh, they can get pretty aggressive when broody, watch your hands!