Update: DOOM/DOOM 2 v0.02 for the PSP has now been released and includes fixes for a Dpad crashing issue, a rapid gun bug, and the Home button exiting emulator issue in the update!
Today Lantus has released his port of DOOM/DOOM 2 v0.01 for the PSP handheld! Features include: DOOM 1 shareware WAD included for instant action, analog stick movement, save/load supported, sound, and source code of course. Those interested in checking it out can grab it from HERE. Enjoy!