I have noticed that DuoLingo usually wants the top definition and for different sentences sometimes a different word from the word's list appears on top. In this case, although the word can mean gobbler, I would go with the more general term unless I knew for sure that her turkey was a live male turkey.
This is correct. I am an avid wild turkey hunter and only the males "gobble" (commonly heard during the Spring mating season), so males are often called "gobblers". Mature males are also referred to as "toms" or "longbeards". Young males are called "jakes" and females are "hens". Very young turkeys are called "poults" instead of "chicks". These are common terms used by hunters and biologists but the average American doesn't typically know them.