In response to your question, "Can I shoot an animal that is a threat?" as my old high school English teacher would have said, "Sure you
can if you have a gun but,
may you? Depending on circumstances, you might be facing civil and criminal charges. As stated above, reasonableness is the criteria not fear.
A postal letter carrier in Fort Worth killed a 10 pound Yorkie by crushing the dogs head with a stone because he was "afraid" of the dog. It's going to be interesting to see how that plays out. Of course, the USPS is saying the employee was "defending" himself.
