If you read the readme, you'll see that the current version of Doom for PSP needs DOOM-compatible WADs. The FreeDOOM IWAD is BOOM-compatible, not DOOM-compatible. The FreeDOOM devs state in their forum that they are aware of this (as it affects more than just Doom for PSP), but have no plans to fix the issue. It works with BOOM and PrBOOM, and that's all they care about.