In Hamlet's speech, "To be or not to be", what is the dramatic irony?

In Shakespeare's Hamlet, there is
dramatic irony in the "To be or not to be..." speech.

The
speech itself is a question of whether he should go on living or if he should take his
life.

He is deeply saddened at the loss of his father,
finds out it is really murder, that the killer is his uncle—who has married Hamlet's
mother—and the job of seeking vengeance has been charged to Hamlet by his father's
ghost. He also does not want to kill Claudius (his step-father/uncle) if there is a
chance the new king can go to heaven, but if Hamlet kills a king mistakenly,
he could end up going to hell. Hamlet is not afforded an easy
decision.

One irony is that it is a mortal sin to commit
suicide, something to fear; on the other hand, Hamlet suggests that death is to be
wished for, for the peace and release it offers.

It is also
ironic that Hamlet pours so much thought into making this decision—one he cannot make
lightly; if he should end his life, he must consider what he knows, but also all that he
does not know about "the undiscovered country." At the same time he is wrestling with
his decision, he admits that there is a downside to thinking about it too much and
making an educated decision. Thinking too much can make the thinker a coward. So that
which takes courage to do, can also be the thing that robs one of the courage needed to
take the step.

Another irony is that Old Hamlet is dead and
cannot be touched by things of this world. Hamlet is very much alive and can lose
everything in this life, as in the next, by
making the wrong decision. That which will avenge his father's murder is the very thing
that could destroy Hamlet.