Alfie (also 10 months) started doing this with his and making quite a lot of headway into it, and I took it away from him. I didn't want to chance it. I know when he eats bits of twig they pass through undigested, and I'd be worried about undigested wood accumulating in his gut.
Have you seen the thread about the Stagbars? Or the ostrich tendons? (seeing as you have a gnawer!)