The continued media bashing could be a perfect opportunity for a very simple (and cheap) advertising campaign from Qantas.
Get some real front line staff - pilots, cabin crew, engineers, ground staff etc, briefly explaining why go-arounds happen, what causes diversions, and how engine shutdowns/failures are dealt with in a routine matter. Keep it short and simple, much the same way the "On: Q" Plane Talking segment is done that you sometimes hear onboard.
Could be a big "up yours" to the media outlets, whilst re-assuring the travelling public. Problem is, none of the commercial networks would probably play the ads.