Perfect I ligit have everything you just listed LOLQuail are hardy, they'll be fine. People keep quail outside. Many species of quail available in the hobby are closely related to their wild ancestors and would be living outside. Coturnix in particular are adaptable.
Again- if the budgie is happy and healthy, the quail will be fine. Shade and a lot of water when it's hot, sheltered, relatively enclosed places to burrow down into straw when it's cold. Make sure they have a dust bath, a dish of grit, and a dish of oyster shell, all separate.