I think the best advice is to add a fence to set a perimeter or boundary for the birds. Even some quick temporary poultry netting will make a big difference. Dogs can have amazing abilities whether they are pure bred or common mutts. We have a dog pack of 7 dogs on our 20+ acres which has a perimeter fence. The birds also have their own perimeter fence area. 1/2 acre or a 1 acre area will be plenty large for your birds to free range. If you decide to get a dog then you could also fence the 3 acre area to set a perimeter for the dog. Our dogs chase rabbits and deer on the property and without the fence they would continue a chase well beyond the perimeter. Obtaining a dog with special abilities can be time consuming and cost prohibitive. Just my 2 cents worth.