do I have to use cripple studs
There is no code requirement that I am aware of to use cripple studs if they are not needed. I put in two headers in my house, both are steel beams, neither has any cripple studs as the headers are tight against the existing wood double top plate. Or maybe I misunderstood your question?
In any case, you should check with local code official if a door less than 6 feet tall is acceptable, it certainly would not be where I live. Also, how did you size your header as a 2x12? Are you certain it is adequate?