The couple met on set in 2008, when Georgia played David's daughter on the show.
David proposed last Christmas before the birth of their daughter, Olive in March. Georgia also has a son from a previous relationship.
[See also: Rochelle Wiseman and Marvin Humes get engaged]
[See also: Celebrities' Christmas proposals]
The Doctor Who connection extends to Georgia's dad, Peter Davison, who played the fifth Time Lord in the BBC series.
He told the Mail in July: "I suspect that, crucially, Georgia wasn't overawed by David. He's a really nice guy, but a lot of people are intimidated by actors who've played The Doctor. I've been asked to pose for photos with fans who've been shaking beside me, just because I played The Doctor.
"I suspect that goes on too with David, who, like me, is intimidating without doing anything to intimidate. Georgia was able to get over that, partly because she's strong and courageous, and partly because she grew up around an actor who played The Doctor. She was never fazed by meeting TV actors when she was a child — it's second nature to her."
Congrats to the newlyweds!