Yes let her set and hatch her own eggs. Broodiness is being bred out of our quail. Anytime we can let one be a mom helps slow that down. I had a button hen successfully hatch and raise her clutch.
Be prepared to remove the male if he becomes a pest and demands mating while she is trying to incubate. A really good roo will call her to food when she gets off the nest and I've heard some will even set on the eggs while the hen is off, though I've never seen it personally.
Give her "safe" places to lay and incubate where she can be partially hidden. Maybe some greenery hung near a nest box or whatever. While they set they often like to use straw, grass or shavings to build up the nest around them to help conserve heat and hide the nest. Placing these items within reach of a nest will help strengthen the urge to nest and gives the hen something to do.
And yes, be prepared for more giant poops!