Mallard Duck

Ducks are picky about location in a way most critters are not. They only appear in the middle third of the world's width, and only where there is standing water on the surface. Size and origin of the pool do not matter, so digging a small hole next to your town and filling it with a Water Bucket is enough to pull them in, and the area near NPC housing counts as valid ground for them. If you built your base near a world edge you will not see any at home and will have to travel toward the center.

A duck wanders the ground until something knocks it out of that mode, specifically falling far enough or going under water, at which point it flips to its flying form. In the air it picks a direction, commits to it for a while, then sets down wherever it happens to be and goes back to walking. It does not try to land on water despite needing water to spawn, so a duck you were tracking for the net can end up halfway up a hill in the middle of nowhere. Net it before it gets airborne if you can.

Any Bug Net picks one up, and the caught Duck or Mallard Duck travels in your inventory to be let go somewhere better. Building it into a Duck Cage or Mallard Duck Cage locks it in permanently unless you break the furniture back down in Shimmer, and cooking it into Roasted Duck is the other exit. A Duck Statue will produce them but not usefully for a collector, since statue critters cannot be netted at all and pop into smoke if you try. Ducks are also fragile enough that any nearby enemy will kill your supply, and negative luck can flip them hostile toward you.