It is rare for puppies or dogs to get poison ivy. Their coats are there to protect them from things like that. But they do have allergies just like us and it is possible. You can give puppies benadryl if they do have a break out. You would use baby benadryl for puppies of course and use the dosage on the package and go by the puppies weight just like you would with a baby. I have to give my dog benadryl quite often, especially this time of year.
Yes, they can get poison ivy and they can bring the plant's oil home on their fur and spread it to their owners who weren't even outside.
Dogs do not get poison ivy but they do get the oils on their coat. So they can give it to you. So be careful if you are allergic to it.