Looking at the wiki entry for The Ark in Space, I can see that the Doctor thought the controls were roughly 30th century, though it's several thousands of years later because their "wake up" mechanisms malfunctioned. The story is about a colony ship that left Earth because of solar flares.
Now if Amy is 1306, guessing a birthdate of 1989ish, the year is around 3295, and if the Queen has been alive for about 300 years, that would bring us right back to 2995/the 30th century.
Proving that Steven Moffat dating is better than UNIT's, and that Nerva Station and Starship UK left Earth during the same disaster. :)
(For those of you who have not seen The Ark in Space, they're getting ready to resettle and rebuild Earth, so the 51st century can happen as planned and produce Jack and K9 for our viewing pleasure.)