You can continue to feed that (since it's non-medicated) but ADD a separate dish of whatever form of calcium supplement you prefer on the side. Ground up egg shell, oyster shell, grit plus calcium, etc. as Chick starters do not contain enough calcium for laying hens. If you opt to grind your own egg shells either do so immediately after you've opened the eggs or bake the shells to dehydrate them (and makes for a smoother grind as well) and then grind them. Storage should be in an air tight container, I use an old pickle jar. Too much calcium in the diet of chicks and cocks leads to health issues down the road. Fortunately, birds seem to be born with this knowledge and those that don't need it, avoid it.
You can also elect to change their feed altogether into plain game bird feed, ensuring that the protein level is at least 24%. I don't see a real benefit to the change since you'd still want to serve calcium on the side.
Either way, when your birds molt, you'll want to increase their protein significantly to speed up the re-feathering process; Grinding some dry cat food (typically 30% protein) and mixing that 50/50 ratio (by weight, not volume) with your normal quail feed, will help.