TwoBlueTails
This is a collection of short stories, each mostly independent of the next. They are all based on how different things would be or not if the Rose novelization book, written by Russel T. Davies himself, had been how the first episode of modern who really happened - as in there, Rose's character has a lot more dept, wit and maturity than her canon televisioned version (in my humble opinion at least).
Each story is structured as either rewrite of a specific scene in the show, or as something that happened in between cannon episodes. They focus on moments of character development on the Doctor and Rose's relationship (or their character), and later on mention of their relationship in the seasons Rose was no longer present to other companions or just as reminiscents of the Doctor on his own.