Either this is an ironic coincidence or an intentional homage, but this song was performed by a Doctor in another science fiction franchise.
http://en.memory-alpha.org/wiki/La_donna_%C3%A8_mobile
In Star Trek: Voyager, the ship's doctor (also simply known as "the Doctor") performs this song in the episode "Tinker Tenor Doctor Spy."
Two sci-fi shows, two Doctors, the same song.