A standard and common definition of murder that I found:
"Unlawful killing of another with intent to kill, or with wicked recklessness to life."
I believe that Honey Girl's death qualifies under that definition.
Only because you left out part of the definition.
mur·der noun 1. Law. the killing of another human being under conditions specifically covered in law.
While killing an animal may very well be illegal (and was in this case), it is not murder.