You realize birds carry a LOT of different types of bacteria, etc, right?
The rabbits probably carry lots of bacteria too.
But whether quail-bacteria hurt rabbits, or rabbit-bacteria hurt quail, I don't know. Many kinds of bacteria are pretty specific about what things they cause trouble for.
Im building an aviary for my quail, and was wondering if I could keep some or all of the does with them? If it was big enough? Or would the rabbits eat the quail? Just a thought and figured Id come here with it before putting too much energy into an experiment.
You could put the quail in, then put a single rabbit in and watch what happens, then decide from there. I really don't know what they'll do, and it probably depends on a bunch of things like the size of the pen, the rabbit's temperament, the rabbit's size, and how the quail react.
Or you could decide to just house them separately, which would certainly keep them from hurting each other. It would also make feeding easier. Quail food is probably not healthy for rabbits, but the rabbits would be happy to eat it. I expect the quail would mostly ignore the rabbit food.
The other problem with putting more than one rabbit in the aviary: if the rabbits are used to living separately, they may fight each other (bad for the rabbits, bad for any quail that get in the way.)