Wow. It's been a while since I had Doom on my PPC (two years ago when I owned an EM500 as well).
There might be multiple versions out there. The one that I know of was ported by
Jimmy Software. I can't give you a more precise link b/c they appear to be down at the moment, but check their "products" or "download" section. They should have full directions on what to do. I do recall that you still need the original WAD files from your regular PC version of Doom, otherwise you'll be stuck playing the shareware version (the game is provided for free after all).
As for memory not being an issue, let me tell you that with the EM500, memory is almost always an issue, even with an external card. If I remember correctly, while you can install the game on your SD/MMC card, you'll need somewhere around 8-12MB of PROGRAM memory available to actually launch the game (I assume you understand what the difference between program and storage memory... it has nothing to do with external storage). You'll probably need to soft-reset your unit and then go into your memory applet to manually adjust available program memory to this amount and then immediately run the program before the unit readjusts it back.
Hope this helps.