It is possible that one could pursue a Master's of Fine Arts degree with an emphasis on digital media or "new forms" and concentrate on Dr. Who and other similar television series.
It is more likely that one would pursue a Bachelor's Degree in Film Studies. I found five apparently reputable schools that offer such in a very short search:
Doctor---Hugh Laurie, who plays the title role on "House", has a degree in anthropology. He is a diagnostician
The Doctor from the TV show Doctor Who.
Richard Chamberlain
doctor who
Dr. Oz is a doctor who has a tv show.
doctor 90210
Sanjay Gupta
11 i think
John
Doctor Who
Daleks are from a BBC television show called Doctor who
grays anatomy