I tend to agree with Nambroth, who has given you the exact advice I would have. My childhood 'tiel began laying when she was about seven. In her case, at least, the best thing to do was just leave her with her egg and let her sit on it until she got bored with it. This prevented her from laying more eggs (putting her at risk for all sorts of things, as you recognize). She never got egg-bound and stayed quite healthy. Joey gave us two little eggs and then decided this wasn't for her.
Not only is Nambroth correct about the breeding situation in the past, some pet birds will do this when they're bored. Now, Joey was spoiled, more like a puppy than a bird, and hardly ever in her cage other than at night. I'm not sure she was bored. We did, however, provide her with comfy newer perches and also made sure to cover her cage at night (her cage being in the living room) even if we were up late. I think this, more than anything, helped convince her to stop laying.
Good luck! Make sure she gets plenty of calcium; if your girl lays a new egg when you take away her old one, just leave it there for her and don't remove them.
