So...the First Doctor?
Talk about it here.
In a parallel universe, the first incarnation of the Doctor pursued a career as an author before leaving Gallifrey with his granddaughter Susan after spending many centuries being kept as a prisoner as part of a plan to turn him into the next Lord President of Gallifrey, though even in a half-brainwashed state he wasn't interested.
He had two great-grandchildren - a boy and a girl.
After being ostracised by his family, the Doctor desired to escape from Gallifrey in an abandoned Type 40 TARDIS with Susan. However, he was delayed in this action when he was mentally conditioned by Quences at some point to forget about his plans to leave Gallifrey and travel the universe, as part of Quences' plan to be set up as President of the Time Lords. Living in isolation with his robot servant Badger, the Doctor became an author of fiction, writing the first science fiction historical romance, An Adventurer in Time and Space with the Possibility Generator. His other works included A Journey to Ice-Askar, The Winter Star and An Exciting Adventure with the Hassites. His stories were popular with generations of Gallifreyan children.
After several years, he was reunited with Susan, who was the President-elect. At the time, the Doctor was experiencing a simulation of Hannibal's crossing the Alps in the Possibility Generator. Together they discovered that "Auld Mortality" was using Badger to regularly hypnotise the Doctor, so he could be manipulated into the position of President. However, realising that Susan was about to become President, he attempted to control her instead. However, the Doctor used the Generator to release Hannibal and his horde on to the Panopticon, and destroyed Badger and defeated Quences. Upon returning the horde to the Generator, he discovered that he had been living in a TARDIS all along, and had been conditioned to forget it by Quences. (AUDIO: Auld Mortality)
Although Susan remained on Gallifrey, the Doctor decided to become a renegade Time Lord and travel the universe. However, the Doctor used the Possibility Generator to create a facsimile of Susan who decided to travel with him. On their travels, they encountered Thaleks and Winston Churchill. (AUDIO: Auld Mortality, A Storm of Angels) This Doctor had no hesitation in interfering in established events and changing history (albeit in what he believed were minor details that would not affect the wider course of events): he travelled with and taught Leonardo da Vinci the technology of flight which later gave the Elizabethans space travel, rescued the princes in the Tower, crafted a hearing aid for Beethoven, and warned the Aztecs of Cortez' approach. It was during one of these adventures that Susan began to suffer from radiation sickness. When confonted about his interference, the Doctor was oblivious, believing that he hadn't changed history - just helped people. (AUDIO: A Storm of Angels, PROSE: The Innocents)
After a while, the Time Lords (led by the "real" President Susan) began to pursue the Doctor across time to prevent his changing history. While in pursuit, the Doctor and Susan arrived on an Elizabethan spaceship led by John Dee, carrying alien crystals from the asteroid belt. They discovered that the crystals were sentient and were communicating with Dee, pretending to be angels. Their plan was to be presented to Queen Elizabeth I and take possession of her and the rest of Earth. However, after succeeding in stopping the crystals, the "real" Susan discovered the "fake" Susan, who offered her the chance to swap places and travel with her grandfather, while her facsimile could return to Gallifrey and die of the radiation sickness. Susan took this offer, and she and the Doctor left in the Type 40 to travel the universe together. (AUDIO: A Storm of Angels)