Sometimes a duckling is just the "runt" of the litter....I recently went searching for a companion to an orphan duckling that needed to grow up with another duck but was not accepted by my others...so I figured I buy one her age/size so they had a chance of getting along.
Could'nt find one anywhere even close. What I DID find was a tiny female that was 1/2 size of the rest of her hatch of 30, and closer in size to my baby. This runt was feathered, and matured, just undersized. Took her home, and she and the baby have done very well together. The runt (mid size I call her) is the friendliest and gentlest duck of them all. She is fine, filling out a bit after being able to eat and not get beat on by larger ducks. She adopted the baby right away and now protects the little one like her own. They are almost the same size now after 5 weeks together. the baby is catching up fast and will pass her is size by Jan.
Your little duck will probably be fine. Add some fresh greens to her diet and wash off her crusty butt if necessary. I've had to do that before with ducklings that still had more down than feathers. They grow out of that with full feathering and more water time.