Yes but you wouldn't really be playing Doom now would you? I mean, in this new Doom you'd probably be able to jump and look up and down.. But that's not doom anymore cause now the gameplay is different resulting in a different game. One of the cool things i liked about doom is how you could play it without a mouse, making it feel so much faster and ultra responsive than newest FPSs. I actually still play 1vs1 battles of the first level of Doom 2 with my cousin when we get the chance. I know that level better than I know my home to be honest..

Anyhow, you're in luck cause I just googled it and I immediatly found a Doom 3 mod that gives you all original levels, monsters and weapons of Doom1.. It's called Classic Doom.