Looks like a release date for Doom 3 on the Xbox platform is still "up in the air" according to an article at gamesindustry.biz.
Gameplay and technical issues are likely to cause problems for a 2004 release that are looking unlikely to be solved in time. Doom 3 has been extensively tuned for the PC platform - well, certainly for a PC that's the recommended spec. And this spec is something that the Xbox falls short of, itself being a 733Mhz Pentium processor, a GeForce 3 chip and 64Mb of shared RAM - which is far below what's required of a PC to run Doom 3 acceptably.