FDA Advice
Poison ivy and other poison plant rashes can't be spread from person to person. But it is possible to pick up the rash from plant oil that may have stuck to clothing, pets, garden tools, and other items that have come in contact with these plants. The plant oil lingers (sometimes for years) on virtually any surface until it's washed off with water or rubbing alcohol.
The rash will only occur where the plant oil has touched the skin, so a person with poison ivy can't spread it on the body by scratching. It may seem like the rash is spreading if it appears over time instead of all at once. But this is either because the plant oil is absorbed at different rates in different parts of the body or because of repeated exposure to contaminated objects or plant oil trapped under the fingernails. Even if blisters break, the fluid in the blisters is not plant oil and cannot further spread the rash.
Tips for Prevention
Wash your pet if it may have brushed up against poison ivy, oak, or sumac. Use pet shampoo and water while wearing rubber gloves, such as dishwashing gloves. Most pets are not sensitive to poison ivy, but the oil can stick to their fur and cause a reaction in someone who pets them.
Wash your skin in cool water as soon as possible if you come in contact with a poisonous plant. The sooner you cleanse the skin, the greater the chance that you can remove the plant oil or help prevent further spread.
per FDA Here