I have a dog that I take everywhere with me and she gets in to poison oak way more than I wish she did.  I use a product called Tecnu to clean her coat and it works very, very well to remove the urushiol from the fur.  It says on the Tecnu label that it can be used on pets.  The stuff is truly great in my opinion and I've used it on myself for about 10 years. I'm not sure which stores carry it but I've bought the big 12 oz bottles of it at Rite Aid and CVS.