The study of how animals behave is called ethology. If you're interested in the way baby ducks imprint on their mother (or a substitute for their mother), you might want to consider studying ethology.
The general study of animals is zoology, and ethology is a branch of this science that centers on behavior. Ethology's focus is on behaviors (observed in natural environments) that evolved to help animals adapt, and this field often overlaps with psychology and the study of human behavior. The original 17th century definition of ethology was "mimicry," but by the late 1800s it came to mean "the science of character formation in animals."