Well quail do best on a gamebird specific feed with free choice oyster shell from what I hear.
Most people around here feed game bird starter mixed with a bit of layer feed for the calcium, though quail seem to tolerate not having much calcium supplementation better than chickens in some cases.
Mixing oyster shell in layer feed is basically double dosing them with calcium, that isn't ideal for non laying birds (particularly roosters) since they aren't able to physically shed the extra calcium in the form of egg shells.
Feeding layer feed is fine as long as the oyster shell is in a separate container and if the layer feed is not the staple of the diet. Mixing 80% Gamebird starter with 20% layer sounds like a good combo.
JMO