It is quite rare for a typically coated dog to get the significant contact dermatitis as humans do (hairless dogs can get it, however). Their coat is extremely protective against this sort of thing. What commonly happens is that the oil from the plant rubs off on the dogs coat and then gets onto your skin when you touch the dog. This is not only the case with dogs, but with other animals - especially horses.
Sometimes a small amount of the oil does get down to the skin but even then, there's usually no need to treat it. Also, dogs will sometimes lick the oils off their fur but even that doesn't usually cause problems. However, if your dog shows any signs of anaphylaxis, that's a life-threatening situation that requres an immediate visit to the vet or emergency clinic.
if you are worried about the minor itching, your vet can give you a topical to control it, but honestly speaking if that's all thai is happening I wouldn't bother (unless you have a hairless dog).