I finally got round to doing a bit more research on our visa requirements for the trip. I was getting ready to get wrapped up in documents and red tape, with different hoops to jump through for each border. But I was amazed. The only countries that we need a visa for are the first two on our journey: China and Australia. And while the Chinese visa will require us to travel to Dublin, we can apply for an electronic one, online, for Oz. Nice one! I think if we had tried this 20 years ago, the Irish passport holders amongst us would not have found this so easy.
New Zealand, Fiji, Chile, Bolivia, Peru and Argentina (actually - I'm still waiting to hear back from them) fling their doors open for the Irish and the Italians. Yaaaaay!
(Update: the Argentine Embassy has confirmed that for 90 days or less there's no visa requirement for any of us.)