Just spent a good amount of time labbing this match up with our top Scorpion player. IMO:
Without Scorpion's j1, the match up would be 6:4 in Doomsday's favour.
Because of the j1, the match up is at best 4:6 in Scorpion's favour. Possibly, worse.
Doomsday cannot properly anti-air the j1, and the j1 beats splash, leading to a juggle combo. You can punish a blocked early j1 with d1, Es once he lands, but if he cancels the j1 into MB teleport, you'll be the one getting hit and comboed instead.
This means that anytime you're within j1 range, Doomsday can't effectively anti-air and can't attack with jd+3 without running the risk of running into a j1. IMO, Doomsday must try to play this match at a very specific range- just outside j1 range. From here, you can look for spots to dash forward d1 or shoulder dash in and can defend against most of the stuff by holding d. At any other distance, Scorpion has a clear advantage in the match up.