A deerstalker was a type of hat.
The Fourth Doctor wore a deerstalker of tan and scarlet tartan as part of his detective outfit. (PROSE: Nanomorphosis, Evolution; AUDIO: The Merfolk Murders; COMIC: Gaze of the Medusa; TV: The Talons of Weng-Chiang)
While posing as Sherlock Holmes, the Eleventh Doctor wore a deerstalker hat of brown and black houndstooth tweed. (TV: The Snowmen)