The irony in "Hamlet" is dramatic irony, which is different from situational irony; dramatic irony is the difference between what the character believes and what the audience knows. Situational irony refers to the character behaving in a way that is contradictory to the way they are expected to act.
Sometimes situational irony is referred to as dramatic irony, but they do have different definitions. An example of situational irony would be the minister in "The Scarlet Letter" who commits adultery. An example of dramatic irony in "Hamlet" is the fact that the audience knows that Laerte's weapons are poisoned, but Hamlet and others involved are not aware of it until later.