This is my corurnix set. The cage on the side houses 4 males. The big cage is 5'x3', has a dust bath, box for hiding/nesting, plenty of good food and water. Oyster shell free choice. The main cage houses 15 females and 3 males. I'm soon going to build an 8'x2' 3 tier pen for them.
Coturnix set up
3 things typically cause quail to stop laying:
Lack of light (typical advice is ~14 hours a day) - they could have been on supplemental light where you got them?
Lack of proper nutrition (usually 25-30 % protein and 'oyster shell free choice' - make sure it's small enough for them to eat though).
And the most usual cause when moving them: Stress. Moving causes stress, it's more strange if they continue laying than if they stop. But one thing you might want to consider changing, is having multiple males in the cage. One male for 3-7 hens and only one male per cage is what I usually hear (I don't have coturnix). Multiple males per cage = fighting = stress. So I'd split the females up between the 3 males in different cages.