Some lines wont lay as quickly as others so until theyre 12 weeks old i wouldnt worry. Also moving is a huge stress and could still be the issue. Or predators could be bothering them in the night. Or possibly your dog or cat if you have one. If quail arent laying, they arent old enough, arent getting enough hours of light, or are stressed out.
Shade should be ok. Its light hours in a day that trigger metabolic process like egg laying. Where are you located? You may need to add a couple hours of light depending on how much youre getting. 14-16 is the magic number