You may be surprised how well she feathers out once healed, very often you can't tell that anything happened. Picture attached below of one of my hens that was scalped. Skin was completely gone, her skull was visible. The picture is once she just started feathering out, and once they were all in you could not tell anything had happened. It's a much smaller area than your birds wound, but it's really amazing how they heal up.
I understand about the dog, I have two. One is a great Pyrenees, he doesn't consider birds a threat and they are too much work to chase, they're just treat dispensers (he's a poop connoisseur

), and my other is a rescue dog that is a pyrenees/rough collie mix, which is an absolutely terrible combination. Despite all efforts (LOTS of effort), she loses her mind over any kind of bird at all, chases buzzards circling 100's of feet overhead. She's just simply not allowed around the birds. Luckily we have the space to make that happen. Training can help immensely, but with some dogs and some behaviour it's difficult to overcome genetics, so sometimes it's management rather than fixing. Poodles are generally pretty smart, so you are fortunate there! Good luck!
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