Can animals transfer poison ivy oil (urusuiol) from their fur to humans?

Yes, be careful, because you can get the rash from your pets. Since the animals' fur protects their skin from the oil, they won't get the rash. However, the oil will remain on their fur and will contaminate you when you touch them. You can use Tecnu to bathe animals. Apply Tecnu to dry fur, rub in, and fully rinse.