What is the minimum height for garbage disposal drain above the drain stub
I don't think there's a code imposed minimum, but there's likely a physical limitation based on available fittings.

Between the disposal outlet and the drain, there must be a trap.  The bottom of the disposal outlet, must be above the trap weir (the point in the trap at which water starts to drain from the trap).   

Therefore, in theory the bottom of the outlet has to be just slightly above the bottom of the drain.

In reality you'll have to use available fittings, so the minimum height would be based on what the fittings physically take up. Bare minimum, you'd exit the disposal with a 90° elbow, and connect directly to the top of the P-trap.  So whatever height is taken up by the elbow and P-trap, would be the minimum.


  WARNING: I have not searched through plumbing codes, so I could be wrong about a minimum height not existing.