I don't know how the rapid sliding that is DOOM's movement would go in a virtual space, but good God do I want to try.
It's possible thanks to an update to GZDoom, one of the many open-source remakes of the iD classic.
GZDoom was updated to work with the Oculus Rift years ago, but it's only been updated this week to support the latest SDK for the Oculus Rift. That means it's capable of working with the consumer version of the headset, offering users a more comfortable and higher resolution experience than was possible a few years ago.
But so you get an idea of how DOOM functions in VR, here's what that initial build looked like.
The 1.8.10 patch for GZ3Doom is available from Github now. You'll need Oculus Runtime 1.3, DOOM's original .WAD file which you can get from the Good Old Games release, GZ3DOOM and, optionally, a wireless controller. Although I'd just use mouse and keyboard for old times' sake.