She is probably suffering, but I don't think that that is a reason to put her down. Animals have an instinct to live, and she may heal on her own if you give her time. As long as she is eating and drinking, she aims to survive, so don't interfere as she tries to get better.
On Friday morning a bobcat awaited my ducks and chickens when I let them out of their pen, and it killed 10 chickens and injured one duck.
The duck has bad bites on its shoulder and stomach, and she is having difficulty lifting her head. She usually just lets it hang when she is standing or...