Unfortunately, I don’t know what type of antibiotic to use either.
On a side note, can the duck bend its leg on its own? It looks like it might be a minor sprain. I suggest putting her on a stable, flat surface to minimize possible stumbling blocks. (Keeping her in a kennel with the tray or in a clean coop with a thin layer of shavings would be good.) If you could keep her off that leg, that would be great, though it could cause her extra stress or "air-swimming" that'll cause her to further injure her joint. I'd give her two to six weeks on heal time. If she doesn't start showing improvement by the two week mark, it could be more serious, such as inflammation.