"Unless it's a massive professional drone surely the mass is way less than that of a duck, which planes are designed to be able to cope with?"
It's not mass on it's own that's the problem, it's mass *and* density. Otherwise you would be able to prove that a drone is a witch by seeing if it weighed the same as a duck.
Anyway, planes cope with hitting a duck by turning around, landing (hopefully safely) with the fire crews in attendance and then having expensive repairs done. Of course, you could armour plate the aircraft, so you could hit as many ducks as you liked unless you ingested one in an engine, but then you'd have to carry a lot less passengers.