The biggest problem is the size, because the quail are eye-level with the chicks vents. That can cause big problems if they decide to pick. Just watch them closely to make sure there isn't any picking. Quail grow very fast, so they'll be the same size in no time.
The key is making sure the new chicks are agile already on their feet. I can put day old chicks in with 4 week old chicks (all coturnix or an assortment of different chicks species and breeds) in the same big brooder as long as I follow that guidline. I make sure the chick isn't the "im just hatched and sleepy and wobbily" that makes them a target for the spunky older chicks (even by just hours)! And then toes can be bloodied as well as beaks and as Shelley said vents. Though I've never had a vent issue when it has happened it's always mainly bloodied toes from them grabbing the helpless chicks and TRYING merciliessly to EAT THEIR TOES
But as long as they are running around eating and drinking they will fit right in with the older quails and even chicken chicks. Done it many times
I have two 4 day old quail chicks in the brooder now & put 2 of the new born chicken chicks in with them. The new chicks are not on there feet yet but the quail won't go near them. If I would have read Monarcs' post earlier I would not have put them in there but since they are already I think I experiment.