To dupe animals in Dinkum, you will need a Simple Animal Cage which can be crafted at any crafting table with one Tin Bar, one Mangrove Stick, and one Old Spring.
Take the animal cage and trap the desired animal. Only animals that can break out of the cage can be duped.
Wait for the animal to shake the cage four times, and then quickly pick up and drop the cage. The goal is to drop the cage about one shake before the animal breaks out. Unfortunately this part is completely random and the animal take anywhere from three to seven or more shakes to break out. Four was the number that worked the best for me.
If done correctly, two animals will spawn once it breaks out of the cage.
It does take some time, so keep trying!
You can trap the animals by building a dirt wall two blocks high. The animals may despawn after sleeping and they will definitely despawn after quitting and reloading the game.
You can either kill the duped animals for resources or send them in to be researched in exchange for Dinks. Honestly, this is not the best method to farm Dinks as mining in the shaft is simply better.