Hayan Ma-eum Baeggu

Sol and Dong live with their widower father on an island village, where he works as a fisherman. One day a white puppy enters their lives. They adopt him and name him Max. However, after their father dies at sea and circumstances separate Max from Sol and Dong, Max must find the will to fight his way home, so he can be reunited with his owners.

(Source: THEM Anime Reviews)