So Harry couldn't use a simple, explosive spell to take out the alpha? No minds or souls required; there isn't even a trajectory or solid projectile the alpha could intercept. Just -BOOM- explosion in the dragon's mouth (ala Quinn + crossbow). AFAIK, RoF dragons are not magical beasts, so I don't think they'd be as durable, as protected against spells, whatever. Mostly, they just seem bullet-proof.
OTOH, does range matter? Does Harry have to be as close as Quinn was? Would he be as agile as Quinn to avoid a fire attack? Could he cast a spell as quickly as pulling a trigger? Does Harry have shield spells he could cast beforehand?
Seems to me there are a number of variables here to consider. But generally, ideally, I see Potter taking this, maybe even one-shotting the alpha, making this confrontation almost spite.