Yes, your answer is correct. There are actually an infinite amount of counter examples (because the number of objects are indefinite) that violate the statement as the entire sets don't need to be isomorphic and there are only two possible properties A and B, if two objects in P both have the same property, they are equal and thus if one of those objects in P equals some other object in Q, then they both do. So the only scenarios in which the statement is actually correct is
1. There is an object in P that only has property B
2. There is an object in P that has both property A and B but no object in Q that has property B
3. All objects in P have property A and all objects in Q have property A and B.
Does this logic make sense?