Well, I'm about to make myself really popular at this party.
This poor animal is beset by a suite of congenital defects that have her suffering every minute of her short life -- the bill defect, the failure to thrive, the skeletal deformities, the cranial deformity that is suggestive of an underlying brain defect.
That stinks, that's not fair, and that's Nature. This duck lost the healthy life lottery, and nothing veterinary science can do will make her whole or pain-free.
By prolonging her life, you are prolonging her suffering, which is irremediable. Why? For her benefit? So you can "love" her? So you can congratulate yourself, and be congratulated by others, for your kindness?
One of the things I envy my animals is their right to be relieved of suffering when it becomes irremediable, and my duty to relieve it. That's no different for a deformed hatchling than for a beloved twenty-year-old cat. It's the hardest duty of a compassionate animal owner. But a duty it is.
Take this poor little animal to the vet and have her euthanized. Please. For her sake. It's a lonely, and ultimately losing, fight that she's waging.