2x3 is fine. The recommendation is 1 sq. ft. per bird, which would be 2x5. However I have had 12 jumbos in a 2 1/2 x 3 cage, and they got along just fine. My other pens are all 2x2, and have anywhere from 3-6 birds in them right now. Most had 5-6 this summer, but I've decreased my stock on some.
Coturnix do not need very much space, I think more of a 1/2 sq. ft. per bird is adequate.
I would not keep coturnix on a solid floor. They just poop too much. You can have them on wire with a solid floor below, for ease in cleaning, but having them on a solid floor creates a number of other problems. You would have to clean their pens very often, to avoid poop balls forming on their toes. There are also some diseases that they can get from being in their own poop, I don't remember what they are right off. It's just easier and safer to have them on wire. You would need to still have part of the floor solid, to save their feet, but this can be accomplished by a large dusting pan, or a nest box. Mine all have a 1x1 or 2x1 piece of particle board in their pens, along with their dust pans, so they can get off the wire.