A couple of questions for you. Were they laying before you moved them?
You said you put them in the aviary. Are they on the ground or elevated in cages? They will lay eggs wherever they are standing when the urge hits them. Sometimes they will use a nest area, but usually it's just wherever.
Are you feeding them the same feed as the previous owner? Is it a high protein gamebird feed? Some people feed 28 - 30% protein gamebird for the quails entire life. Some feed a 20 - 25% protein to their layers.
It doesn't take much to stress these birds out. Moving, change of feed, change of cage mates,etc. The hours of daylight and your temperatures are ok. So just give them a few more days.