When I added quail, I avoided keeping them with my chickens (or even near my chickens) for a couple of reasons:
1. I read here on BYC and in other places that there are diseases that chickens may have a tolerance to (because they've been domesticated for so long) that quail don't. The chickens could carry those diseases without being affected by them, but if they give them to the quail, the quail could get really sick or worse. I haven't experienced it personally (perhaps because I've guarded against it), but that seems to be a pretty standard caution out there.
2. I don't think my quail would ever find their way in and out of the coop. They're just too small and, well, "simple." I think they need a space that's designed for them.
If you decided not to worry about the disease potential, I suppose it would be possible to design a coop that would work for both chickens and quail (and maybe yours would work as is), but mine wouldn't. Too big, too spread out. And I can just imaging the quail huddled up under the roost all night getting, well, rained on.