I finally got smoking Daisy and tried it out.... what a trash gun. I would go so far as to say it's the worst gun I've used in this game. It definitely needs buffs in several areas, or a new gimmick like +melee damage since it does have a bayonet mounted on it. I would definitely classify it as her weakest gun with the coolest skin, such a shame :\
All the damage is in the explosive shells. You do the most damage jumping over enemies heads and releasing the shells or slide bombing. You can also just run and drop them off behind you blowing up any pursuers. The shells do a TON of damage. But the actual fired shots themselves are really slow and do about 50 to 70 ish with limited range, only 3 shots and you really have to lead them if they're moving. The primary way to use it, I've noticed, is not as a gun, but as an accessory to her high jump and slide.
Mechanically the gun is fun to use, but is kind of weak as a "firearm".