Quite a few cars do this when braking while reversing. It has something to do with the fact the brake-pad has worn itself into situ while the car has been going in the other direction, then when everything is reversed, the whole thing (rotor and pad/caliper) has to suddenly re-position itself in a way which causes vibration due everything is not sitting to-gether (not sure if I'm using the right description here) or as you accurately put it: makes a moaning sound.
Surface rust built-up thru the night-dew on the rotor can also cause a noise on the first brake the next morning,...however, just to be sure, its not a bad idea to check your pads have not worn to minimum or less as well.
Jason