There are a couple of issues that you need to deal with. They’re not necessarily insurmountable, but they make things a little tricky.
First, you probably don’t have enough points to fly business return or even business one way and economy back. On Emirates, flying one-way to Dublin on Business will set you back 128000 points per person. Flying economy costs 60000 points/person. On Qatar, business is 139000 points and economy is 75000 points. Your AmEx points can’t be converted to Qantas points (unless they’re “Ascent Premium” points), although they can be converted to Emirates Skywards points or Asia Miles which would just about give you enough points for one, one-way economy trip. But most probably you’ll only have enough points to fly economy return, or business one-way.
The second issue is availability. I just had a quick look at the Qantas website and it’s not listing any business class availability on the Sydney to Dublin route in July-August. However, there is a smattering of availability in economy class.
This is just a result of a quick look. Quite possibly, spending a couple of hours searching for award flights using more advanced methods (eg. the multi-city search tool) might yield something that a simple search misses. But as things stand, your options are to either fly economy return, or pay for some of your flights, or defer your trip until you have accumulated more points.
All the best!