Hi Sussex x, and welcome to the Forum.
The problem may be that she will crack or break the eggs. Quail eggs have thinner, softer shells than hens eggs, because they are designed for a smaller bird to sit on them (although it is rare for quail to actually do this.) Even a bantam could easily penetrate them by shifting around with her relatively heavy feet on top of them. However, if you want to have a go, and are purchasing eggs, why not just try a dozen and see how she gets on?
I'm not sure how she would take to such very tiny chicks when they hatch, though - I've hatched coturnix and they are really tiddly for the first week, like those little fluffy model chicks you can get to go on easter decorations. Could easily get stepped on I would think, or even there might be the risk of her rejecting or eating them. And it would be very unkind to take them away from her after they have hatched, with her hormones all primed to look after her chicks.