Well, not completely but in a certain way at least. HorrorMovieGuy recently released his mod Quake Stuff Ultra which is actually a mod that ports Quake 1's weapons, monsters and powerups to Doom, and uses the actual models from Quake, which is a totally new approach compared to the sprite conversions that we already know. The quality and style of this mod is absolutely reliable to the original, looks and feels like a perfect port. This is still in development but as of now most of the stuff from Quake 1 is already included. You can find the download and also some news concerning the content and the plans in the official thread over at ZDoom.org.