I'd suggest getting your lone quail a buddy for winter, because being alone in the garage will be very cold. She will need someone to huddle with (another female or male, doesn't matter) for warmth, or else she could die, depending on temperatures. The more quail, the warmer they'll be.
Mice normally don't harm quail. They're attracted to the quail food and their eggs, but I would try to 'mouse-proof' the cage to prevent a whole hoard of mice poop getting covered all over the quail's cage as mice poop obviously isn't healthy and could be contaminated with all these nasty bacteria's since mice go and eat everywhere and everything.
Try to block holes small enough for mice to get through (if they can fit their head through, then they can fit their body), or even take away the food at night as that's when they're most active. Don't forget to collect eggs daily.