"Run through the Quake campaign as Doomguy," reads the Duake description. "Simple as that!" Well there's a little more to it, but sometimes a mod just speaks for itself. In fact, given the long history of mods for both games, I'm surprised this wasn't made sooner.
Duake is the work of a modder with an amazing handle: Magic Nipples. It puts Doomguy and his arsenal of weapons in Quake, and adapts everything for the vertical aiming and movement of that game. As well as this, it makes a whole bunch of changes to the vanilla Quake experience, overhauling the first episode to add a bunch of fancy lighting, coloured water, new props, some extra baddies and a re-jigging of enemy placements.
There are elements of this that go above and beyond, such as adding two new Doom HUD types and a minimalist HUD based on Doom 64, replacing the nailgun with the rifle, and reworking some of the enemies to have different attacks. It also apparently reworks "the Chthon fight to be much more interesting", though I didn't see that for myself, and has added a bunch of new secrets to the levels.
Magic Nipples says they're not quite done yet, and expect to release some further updates, but as-is this thing works perfectly well: the only slightly odd aspect is controlling Doomguy with Quake's movement style, which is unavoidable but would probably have John Carmack's temple vein throbbing. The project is also open source on Github.
Among Magic Nipples' other projects is one that I covered years ago, Half-Life: Year of the Dragon, which somehow replaces Gordon Freeman with Spyro the dragon. I'd certainly say they've found their modding niche. And Duake is a great name: better than Qoom, anyway.