The only reference to "She" is the golden and he stated that his dad shot her so...
...I think the canine went byebye.
ENGLISH CLASS IS IN SESSION
It makes more sense for the dad to shoot the chicken tho, look at the sentence:
The bird was still alive too, so my dad shot her
The bird was alive, so the dad shot her. Meaning that if it was dead, it wouldn't have been shot. I don't see what the bird being alive or dead has to do with the dog's fate, but it all makes sense if it was the BIRD who got shot, because it was suffering. Another thing, is that "the bird" is the subject of the sentence, and the predicate is "my dad shot her". "Her" has to refer to a previously introduced subject, and while the dog is a her, the bird is the subject of this sentence, not the dog. Also the bird was the most recently introduced subject, which is another reason why the her is referring to the bird.