I wouldn't brood them together as a newborn coturnix quail is about the size of a U.S. Nickel and a newborn chicken is about four or five times that size. Adult quail (6 to 8 weeks) are about equal in size to a 2 or 3 week old chicken. You'll need to not mingle them until they're of like sizes, and when the chickens growth outpaces that of the quail, they will already have solid friendships built between them (no fighting). By the time your chicken chicks are 8 to 10 weeks old, they'll be much larger than your quail. In theory, the quail, being adults by the time the chickens are introduced to the flock gives the quail the maturity to put the chicken chicks in their place early on, giving the quail a higher place in the pecking order. The quail will need that elevated status to overcome the growth rate of the chickens.