Quail are very seasonal layers, so yes, combined with the move, it could be that they have gone off lay and won't lay again until around next Easter. Mine are still laying but are beginning to slow down.
Japanese quail come in a variety of colours so it can be quite difficult to sex them according to colour. I f they are of the "wild type" of colouring then the female will have a speckled chest while the male has a cream/beige coloured front. Can you post photos?
The male has a distinctive "crow" .... though tend not to be so vocal at this time of year and produce a foam ball when sexually mature/active .... again most noticeable in the spring/summer.
I feed mine mainly on layers mash as this is easy for me to get hold of at our local agri store. Think personally that layers pellets maybe a little large for them. Marriages do layers pellets specifically for quail .... you may have a supplier near you? They like millet as a treat and lettuce.
They appreciate a dust bath .... probably more than hens do.
Sorry, given the time of year and the shock of a move it maybe that you have to wait until spring for your eggs.

.... but they are yummy little eggs and quail are prolific layers.