Quail just sleep wherever they are, they don't roost like chickens, so they're very unlikely to try to come back. You may be able to trap them if they're still in the area, though.
Double-yolker eggs usually either fail to develop properly, or one twin absorbs the other. There just isn't enough space for both of them. A couple of people have managed to hatch two chicks from a double-yolker, but the chicks tend to be weak, small, and underdeveloped. It's possible, but...
The egg will not grow into a baby chick unless the hen sits on it, or you incubate it. The hen will not sit on it unless she goes broody.
A fertilized egg is only a few cells different from an unfertilized one when freshly laid. It takes a few days to do anything. If she's not broody and you...
If your quail isn't broody, she isn't going to sit on that egg either way. She's not sitting on it or nesting, so she isn't broody. If you have laying birds, no broody, and you don't want to incubate eggs, take the eggs out and eat them.
Quail don't get pregnant. They make an egg inside their body and lay it immediately, every couple of days, they don't hold a baby inside them like mammals do. You'll know they're laying eggs when you find eggs.
Quail, like chickens and other birds, lay eggs regardless of mating. They lay eggs whenever they ovulate, and most animals ovulate regardless of their mating, with some exceptions (like cats). She's approaching the age of starting to lay, so you should get eggs soon.
Have you figured out the...
What kind of quail?
What do you feed?
How much space do they have?
Are you sure they're fighting, and it's not that one is trying to mate and is clumsy about it?