i) births and deaths

19 September 1925: birth of Dallas Cavell, who played the road works overseer in the story we now call The Reign of Terror (First Doctor, 1964), Bors in the story we now call The Daleks' Master Plan (First Doctor, 1965), Trask in The Highlanders (Second Doctor, 1966-67), Sir James Quinlan in The Ambassadors of Death (Third Doctor, 1970) and the head of security at the radio telescope in Castrovalva (Fifth Doctor, 1982), getting steadily less hairy as the years went on..
19 September 1940: birth of Caroline John, who played Liz Shaw, the Third Doctor's companion in 1970.
ii) broadcast anniversary

19 September 2015: The Magician's Apprentice kicks off the ninth series of New Who, bringing back Davros and introducing Missy. And the Doctor plays the guitar.
iii) date specified in canon

19 September 1835: The Sixth Doctor and Evelyn encounter Charles Darwin and the Silurians on the Galapagos Islands (in Bloodtide, a 2001 Big Finish audio - one of their best, IMHO).

19 September 1981: possible birthdate of Toshiko Sato (Torchwood).