Fan Fic / My Little Timelord
The Doctor and his lovely assistant, sharing a moment.

The mysterious Doctor Whoof and his wonky-eyed companion have vanquished the Dalek-Cybermen Alliance and saved the citizens of Ponyville from the wrath of their evil plot! But, as Ponyville rebuilds, ponykind finds itself under attack. Never before seen creatures are bleeding through from the darkness, their origins unknown and their intent indecipherable.

The Doctor and his companion have disappeared, and ponykind, scarred by war, must defend itself. From the ashes of that dark conflict a new order has arisen, tasked with protecting the future. Torchwood: outside the Monarchy, beyond the Royal Guard. Equestria’s fate hangs in the balance.

This fic was one of the first, and certainly is one of the most popular, Doctor Whooves and Derpy ship fics to ever be written. In true Doctor Who fashion, it features extra-terrestrial invasion, time travel, and a Torchwood offshoot.

The fiction may be found here.

This My Little Pony: Friendship Is Magic Fan Fic provides examples of these tropes:

  • Dead Fic: The last update was the December of 2011, with the promise of an update sometime before the end of January 2012. There has not been any activity since 18 January 2012 and the author is by any means uncontactable and untraceable. This trooper fear that she may actually be dead like her fic.
  • Death Ray: The Daleks just wouldn't really be complete without them.
  • Fandom Nod: At one point, Ditzy sees a younger version of herself and calls her younger self Dinky, and seems convinced she is hers and the Doctor's daughter.
  • Fate Worse Than Death: When Twilight Sparkle takes over Equestria, she banishes Princess Celestia to the sun. As the spell automatically wears off every millennia, she has to be re-banished every thousand years. The Doctor arrives at the millennial anniversary of the event, just as she came back burning and screaming, and is threatened to be banished with her is he does not cooperate. Keep in mind, she's immortal and had to suffer many thousand years of agony burning in the sun.
  • Mayfly-December Romance: Pinkie comments that the Doctor may be a little too old for Ditzy. That is an understatement.
  • Shipperon Deck: Pinkie seems to think Doctor and Ditzy would make a great couple, while Dash presumes they were already dating, much to Ditzy's embarrassment.
  • Spin-Off: Just like in the TV Show, Torchwood is established to combat any future alien attacks.
  • Word Salad Horror: Ditzy is quite prone to this due to her condition.
    Ditzy: The upside down metal wastebaskets, they're here, they're going to kill us all.