In a small pot, warm the chicken broth over low heat.
In a large skillet, melt the butter over medium heat, then add the rice and barley and toast for 3 to 4 minutes, stirring occasionally. Season the grains with the nutmeg and stir in half of the warm broth. Cook until the broth bubbles, about 5 minutes. Then add the turkey, crumbling it as you drop it into the skillet, and cook until the liquid is absorbed by the grains, about 5 minutes. Stir in the remaining broth, 1/2 cup at a time, allowing the broth to be fully absorbed before adding more. Cook until the barley is tender, about 18 minutes.
Stir in the pumpkin puree. Cook over medium heat until just heated through, about 1 minute. Season to taste with salt.