The driving time between Delhi and Agra would 3-5 hours depends which highway u choose and also depends on the weather conditions...it gets foggy in Dec.It is going to be a good idea to be there at the Taj as soon as possible during the day time....If sun light is there u can visit Mehtabh Bagh at Dawn.....if time permits Fort can be done on day of arrival.
There is a possibility of buying tickets in advance. u need to be in Agra to buy the tickets in advance ...it cannot be done online.
Dec is the peak of the season u may face some crowd.
Thanks and Regards