I think I have poison oak in a corner of my yard. I've compared it to the online pictures but I'm still not certain.
Go to this link with detailed information about and a description of poison oak which may help you definitely identify the plant in your yard.
Dogs do not seem to be sensitive to urushiol, the allergenic oil of poison oak and poison ivy, but it is carried on their coats after the animal comes into contact with the plant. This, in turn, does affect humans when the pet, after brushing the plant, comes into contact with someone. Here is a link that goes into greater detail of how poison oak and poison ivy affects pets.
However, there is some evidence that pets may develop rashes on areas that are not protected by a thick coat. Here is a link that addresses that issue.
We hope that neither you nor your dog gets a nasty rash!