A Death Knight will be a new character you make after doing a series of quests on another character.

Take your Hunter example.

Swedehunt does a chainquest and unlocks the Death Knight character (I imagine there will be a picture greyed out on the create a character screen old school style, maybe with a little lock on it).

Then you go to create a character and their will be your option for a Death Knight which fills a _new_ slot. So you'll hvae Swedehunt and Swededeadknight or whatever.

Hunt doesn't become the death knight.