I don't know about quail but I brooder my turkey chicks with chicken chicks. The chicks come out of their shell scratching and pecking while the turkeys are waiting for someone to teach them to eat and drink. In my opinion, and by far I am not an expert, turkey chicks seem very immature compared to chicken chicks. They may be larger but they don't have the savvy that chicken chicks do. I don't know about Quail but I imagine them to be smaller than chickens. I don't think the size difference is going to be an issue. The Quail, being wild birds, probably have great survival skills compared to turkey chicks.
I have Ridley Bronze turkey chicks and so far they are not aggressive in the least. At one month old I separate them from the chicken chicks and put them with my other older turkey chicks. None of the older Turkey chicks have shown any aggression towards the younger turkey chicks. Because I only have one brood hen, I put five turkey eggs into the Bator each week.....then a week later, I add two chicken eggs and my next five turkey eggs (as you know Turkeys take 28 days to hatch and chickens 21). I move the eggs that are ready for lockdown to another Bator. By the time they have hatched, I have just enough time to clean that Bator before the next seven (5 Turkey eggs + 2 chicken eggs) are ready for lockdown.