Ok well since its 60 outside you can them out at about 4-6 weeks and they should be fine and try to take them out for the day and bring them in at night for two or three day to get them used to being in the colder weather
So I disagree with the whole march and april thing I have quail laying right now and it is only the beginning of march its just when your quail are getting enough nutrition to lay eggs make sure thay are getting bug and stuff oike that for them
You can totally put some babys under her and she will be just fine thats what we did a few years back and she went broody every year after and she actually hatched her own after that so just try putting a few very young babys under her and see what happens