Sally - I'm sorry no one has responded; I was offline at a conference. Anyway, what sort of injury was it? Did she lose part of her bill or have a hole in it or what? If she lost part of her bill, it will not grow back. However, if it's less than half gone, generally the duck will still get a long okay although she may need to have a deep bowl for her food or have it floated in water while the bill is sore. If she has a hole in the bill, again this may not close over but if the hole doesn't go through to the mouth (feel along the roof of her mouth to see if you can feel the hole inside), it should be okay. You want to make sure she has good clean water to drink (I know this means changing it often as ducks get water so dirty) to reduce the chance of infection. I have seen several duck bill injuries and all have survived well. One goose lost 2/3 of her upper bill but is able to eat from a deep bowl and does all right. One duck lost a corner of her bill and after the time of healing where it was sore, she does perfectly fine and seems normal. One of my ducks was bitten on the bill by a snapping turtle. The vet wasn't sure whether she would lose the 1/4 or so at the end where there was a big gash that bled terribly. But the duck healed up - her bill looks a little different and has an extra hole in it but she eats and acts perfectly normal. She was on antibiotics (baytril and clavamox) for 7 days since snapper bites are so infectious. I think your duck has a very good chance to do well. You may want to re-think her housing to protect her a bit more. I think it's pretty common for them to stick their bill through wire and this often can lead to injuries. Best of luck.
-Chick Mom/Marlys in Oklahoma