Yes, game hens are seasonal layers, as others have said. She will start laying as the days start getting longer. Probably mid to late January, or February, maybe. You are wise to look for eggs in places she likes to go when she escapes. The game hens I've had loved to lay in the most camouflaged places, sometimes far from their coop. They are all about laying a clutch and then sitting and hatching it, so don't be surprised if she goes broody soon after starting to lay.
