I would put them in an old egg tray (or similar) and stand them somewhere dark and not too cold (You don't want them to freeze). By March I would expect them to have developed sprouts (Chitted) and you can rub off all but one or two and plant them. They will probably shrivel a bit, but not to worry, it won't hurt them. The worry about using your own seed potatoes is disease, commercial seed is grown out of reach of it, but it tends to be exaggerated, probably by those who want to sell seed potatoes. Still, it is worth being vigilant, don't save anything that doesn't look 100%, and I am assuming your top growth all looks fine and healthy.
I noticed one of our American members who lives where he gets two crops a year saying that he was replanting all the small potatoes he had just dug as a quick crop, so no, no dormancy required, and they will get at least two to three months out of the ground anyway.