The average eagle can pick up and carry in flight a weight of between 3 to 4 lbs which is not all that much.
So while an eagle might be able to lift a small dog such as a Chihuahua or a cat the eagle would not be able to lift and carry in flight a larger dog or other larger animal.
Eagles can only carry a small percentage of their weight so an eagle would not be able to lift up or carry a goat or anything else that is large and heavier than it is.
Eagles do however feed on dead goats, dead sheep and other dead livestock but they do not kill the livestock nor can the eagle carry them away.
An Eagle could likely carry a chicken away and kill them but no large animals.