Her song has no irony in it, however it is ironic that she would title a song as such when there are no actual examples of irony.
I believe that was Spoony’s entire point. 
Oh, I know, I know all too well.
Cid gets a cookie.
I was being retorical!
So, uh, is there an Alanis Morissette song called “Irony” or something?
Ironic. It’s probably her most famous song (although arguably “You Oughtta Know” was the one that really gave her her 15 minutes of fame).