I don't know what kind of relationship you have with your vet, but you may just call them and ask. Ours give plenty of free advice.
I called my wife, and she said she did not remember that we had given benedryl to our goats, so I guess I was wrong.
She said we had given to one of our dogs before.
I don't see why it would be a problem, but you should probably ask your vet, unless someone else knows for sure.
Most of the vets around here don't know a lot about goats. But i read somewhere on line that you can use benedryl on goats, it said for a kids use 5ccs.