Quail will stop laying when you move them, maybe for up to 2 weeks or so. If you bought them less than 2 weeks ago, I'd say that's probably what's wrong. If you've had them for the whole 3 weeks, then it could be something else, such as stress as James suggested, causing the lack of eggs. Looks to me like you have button quail, AKA chinese painted quail, King quail, latin name Coturnix chinesis (not to be confused with the larger "Coturnix quail" that others keep - these are Coturnix japonica or something like that, otherwise known as Japanese quail). The one in the picture with the white bib is male. It is difficult to tell with the silver/white ones in the background, but if there is a clear white bib then that means male. Obviously in an all white bird that won't work. You say you have 4, but I can only see 3 in the picture. Is the 4th one brown? If so you should now be able to tell if it is male or female. Do you know which ones were laying in the shop? If there were 2 laying then it's likely you have 2 males and 2 females, or 1 male and 3 females with one immature female (possibly the "little one"?)
In america most people keep buttons in pairs, so you could maybe separate them into 2 pairs (making sure that they are in male/female pairs, otherwise there may be fighting) and this could help relax the hens and start them laying again. However over here we're told to keep them in 1:3 ratios, so if that's what you've got then I'd leave them be.
Make sure that there are plenty of hiding places, I can see that there's one under the rocks but maybe add an upside down box with a door cut out of it and some silk plants or something, as sometimes hens won't lay if they don't have a safe place to lay in.
If all else fails and you're sure of the sexes, then add some more space. Maybe try one of those big guinea pig cages with the wide plastic bases, as I've always found that with any animal, more space makes them happier.
For the white/silver ones, the only way to sex them might be to listen out for crowing and watching for eggs.
Good luck!
P.S. - I'm sorry if I've just repeated everything from the other thread about sexing, I should have read that before posting, but time is short.
