I let my broodies do the introducing....and I'd give her a couple more eggs. Single chicks have a rough life if something happens to mama or when mama decides she's done. Mama will (or at least should) protect babies. I have one who hatched out on the hillside last summer, brought babies into...
Nothing says she has to hatch HER eggs. If you have fertile eggs from other hens who have good traits you like, you can put those eggs under her instead.