it will be letter B, letter A is a good option but we never use el uno de diciembre when talking about a time that will soon come, if ti were for a time that already passed then yes... But in this case it is asking in the present time when is your birthday... Its like in english if they ask you when is your birthday will you say december first or december one, well you would say december first, that is what letter B means in english Es el primero de diciembre means it is on december the first and letter A is es el uno de diciembre and that means is on the one of december
Hope this helps
