I (netrix) have had this sitting around for a while, but I've been busy with more important things. I don't want to detract from meetpatty's hard work, but it motivated me to release my port. I used the "DoomPSP-0.04 S.S. b5" PSP port. Unfortunately, I will not be able to do feature requests or provide extensive support due to the lack of free time.
Information
WAD files go in "cache0:/VitaDefilerClient/Documents/WADS"
Supports official WADs only.
Audio does not work yet.
Press L + R + Start while playing to access control settings.