Yep dogs have to be in the same enclosure as the chickens, otherwise the eagle won't care. My dogs see them approaching and won't let them land, they chase them when they fly over. An eagle could in theory still grab one quickly and fly off with it but I would be really surprised if that...
I have two livestock guardian dogs and they're fantastic. They see everything and they'll run into action when even a crow flies too low. They're well worth the time and investment, and they're fluffy and adorable :) Good luck!