What is my cat doing to the dog?

The cat is letting the dog know that it loves it. It is also marking its territory. Cats have scent glands on their heads so it is rubbing the dog to put its scent on it. If you know that the dog will not hurt the cat you might want to let them establish tolerance boundaries. I am sure this more than likely goes on when you are not there and they are both fine so give it a shot and see what happens.