If you are talking about a chicken setting on corturnix quail eggs to hatch??
I am not sure it would be wise- the Quail only go for 16 days not 21 and they are very easily broken- not as tough as a chicken egg. The Quail are much smaller. Now if a small light weight breed was broody --maybe!?
They can go broody on anything. One of the other members posted about a hen brooding a plastic dinosaur and a teenage mutant ninja turtle action figure.
Whether the eggs will survive being set on by a hen, even a bantam, I don't know. Can you cushion the nest somehow? Maybe a dished out piece of foam rubber, covered with a cloth so the hen doesn't eat the foam? Maybe one of those little padded beds for a small dog would work well. Maybe have a second one to trade out if any eggs break and you need to wash it.
If I wanted to try it, I'd maybe put marbles under the hen for the first 5 days, then switch them out with the quail eggs. That way she'll have been setting for 21 days when they hatch. I have no idea if she'll accept something as small as a quail chick, but she might. Bantams can be extremely maternal.
Oh, and I'd definitely isolate her from other chickens, so she won't have other hens climbing in to lay eggs, or roos bothering her on the nest.