Most domesticated quail have lost the broody instinct. Some will occasionally show signs of going broody and start to sit but seldom follow through. Your better off using artificial incubation.
I would leave the eggs let her sit and as a back up keep the bator on and a close eye on her that way if she stops you can quick toss them in the bator. I have two buttons sitting eggs right now and I have a friend button quail heaven that has had them hatch there own eggs if you go to her site you can see hers with its 16 babies! Too cute.
I've been trying to get mine to go broody with no luck. You'd have to keep a cage full of tall grass and overhanging branches to simulate their natural habitat, or else their pea brains don't trigger into nesting instinct.
-Spooky
I plan on letting a chicken hen hatch and brood quail chicks this spring/summer. My hopes are that a hen-hatched chick will set their own eggs. But I'm with monarc on this, I haven't heard of anyone that has or has had a broody coturnix!