The American Heritage® Dictionary of the English Language, Fifth Edition, in a usage note, describes the meaning of 'irony':
In its nonliterary uses, irony often refers to a perceived incongruity between what is expected and what actually occurs, especially if what actually occurs thwarts human wishes or designs.
(ironic. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved September 30 2015 from http://www.thefreedictionary.com/ironic)
That sense as given could be applied literally, trivially, and misleadingly, to arrive at the conclusion that your response to your friend is an example of irony (an ironic response). Your response will almost certainly be perceived as incongruous: it is not the expected event, but occurs anyhow. Your response also, presumably, thwarts your friend's human wish for a sensible answer. So, your example meets, on the face of it, the requirements for being ironic, as stipulated by the usage note from the American Heritage® Dictionary.
However, the usage note continues:
People sometimes misuse the words ironic, irony, and ironically, applying them to events and circumstances that might better be described as simply coincidental or improbable, in that the events suggest no particular lessons about human vanity or folly.
So, is your response to the question incongruous, or merely improbable? As it stands, without additional context such that might connect the apparent incongruity of your response with the question that elicited the response, your response seems to me to be merely an improbable event: it is improbable that you would offer such a response as a response to the question. Beyond that no incongruity is evident.
Your response is, however, typical of a literary and conversational device called a non sequitur: your response does not follow from the question. This device, the non sequitur, frequently has a humorous dimension, whether the paucity of logical connection between the non sequitur and what preceded it is intentional or unintentional.
The humor of a non sequitur, as is often the case with humor, defies analysis, but seems to arise from absurdity, in the sense that a non sequitur is
b. Impossible to take seriously; silly.
(absurd. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved September 30 2015 from http://www.thefreedictionary.com/absurd)