I have had cocketiels for several years. It was about two weeks later that I brought Suzi home then she realized they were there... SHe went on a barking frenzy.... ANd just got so excited. My male bird is grouchy, and he snapped back at her... Those birds have been around cats all their lives and are not afraide ! The birsd freddie did not hurt My puppy, and she stills barks at them sometimes.
I don't let the birds out anymore, Suzi would try and get them , it is their instinct.
The wild bird who flew in your house did not stand a chance...