That's terrible, I hope she heals quickly. I sold a couple kids to someone, and a neighbors dog came up and reached through and grabbed the smaller one and pulled him through the pen, thankfully they were there and ran him off before any damage was done. When they talked to the neighbors they said, oh he probably thought it was a squirrel, I think these people were in serious denial. I would have told them if he came back I may mistake him for a squirrel. My biggest problem was their attitude about it, they just acted like they didn't care at all, I bet that would change when Fido didn't make it back home. Thankfully I don't think they had any more trouble w/ him.
My dogs are great w/ the goats. My little dog is afraid of them when they try to approach her, the big dogs are actually abit protective of them, especially when there are new kids. And so far my neighbor's dogs (I only have one neighbor close enough to be a problem), although very annoying, don't seem to have any interest in the goats or chickens. I worry much more about the occational stray passing threw (or one of the farther away neighbor's dogs).