|Yes dogs can get poison oak or poison ivy rash. My friend has a dog that gets a small rash on his stomach where there is not much fur after he runs through poison oak areas. She always takes a rag and wipes his fur off with alcohol. It is an oil cutter and the oil will dissolve into the alcohol on the rag. Go over the area a few times with new rags.
My credentials: I wrote "The Poison Oak & Poison Ivy Survival Guide."