I believe 325 will work for the low level WotLK stuff, but that you'll need 350 eventually.
I'm in the same boat as OP. My current DE alt is a level 36 warrior. The only reason it ever got that high was because they raised the DE cap. I'm going to level a DK specifically to make it my new DE alt. It's a heck of a lot easier than getting levels on my warrior. At a minimum, as soon as I clear the DK starter zone I can get to a major city and potentially train enchanting to 375. Then, with minimal additional questing, I can get to 60 and raise the potential to max 450 (probably won't because I won't need it for DE). Although it will cost me some to level enchanting from scratch on a DK, the time investment will be a lot less than leveling the warrior.