Sorry to hear this, but we as humans, have to remember dog's instincts, hunting as one of them.
Oh, they love field mice,voles,moles,squirrels, and other little varmints too.
I don't like it but do accept it as long as I love my dogs, I know critters like the mentioned and yes, avians, can be targets.
I hope you weren't too harsh with Amber, she's just doing what instinct tells her. Please do not refer to her as a "killer dog" for that.
Sadly, freak things happen. Years ago we gave one of our birds to hubby's friend, her cat got it and killed it.
I wasn't mad at the cat, but was mad at the girl,cause she laughed it off, saying "kitty got the birdy", I was angry cause she was not responsible, it wasn't a freak thing in this case, and not much of an accident, but her ignorance and immaturity to think she could have them together.
I'm sure with your case it was an accident, and hope all can be forgiven in time.
Easy for me to say, but please do not be upset with yourself and/or the dog.
I hope you,your friend and Amber will be able to make amends.

((((((((( SeptemberMorn )))))))))))))