the quail are fine but the rabbit will have to live in the excrement of the other birds. If you want to give your birds nesting material put down some pine needles or some straw. the pine needles work the best!
Straw isn't a great nesting material for pigeons. Pine needles are great as are
tobacco stems which can be purchased pretty cheaply through the supply houses. Might be better to get a rabbit hutch for the rabbits and house