Lord of the Rings is full of fast-travel, actually.
He describes the important parts and any adventures they may encounter along the way, but he doesn't detail every day of each leg of the trip - there are many instances where the traveling parts are glossed over.
I mean, what about the end of The Hobbit where Bilbo travels back to the Shire? Getting to the Lonely Mountain was a good two-thirds of the book, sure (they hadn't visited those locations yet, their world map still had too much fog of war.) But describing the journey back took a handful of paragraphs. If that's not literary fast-travel, I don't know what is.