Well.. All I've read about quail says it's beneficial for them to hatch chicks, because they stop laying while broody and this break is good for their bodies.
For many other birds, however - budgies and such - it's not recommended to let them breed before they are a year old, but this is because producing and laying eggs can be hard on them - and also the feeding of a large clutch can be hard. Quail are laying the eggs anyway, only stopping if you let them go broody (or stress them or deprive them of light) and feeding the young isn't much trouble - they eat on their own as long as mommy shows them how and after a week mommy hardly even has to take the initiative to go eat anymore, they do it all on their own.
In conclusion, I see nothing but benefits in letting her go broody - assuming of cause that she keeps eating. But I've never had a button go weak from being broody and most of mine go broody before they are a year old.