Firstly, don't forget QF and EI are both in oneworld and indeed, EI leased a 747 to QF a few years back, a contract which was regarded as successful by both sides. More significant is the fact that both will, ultimately, operate 330s (QF's from late next year) and since both airlines' high/low seasons fit nicely, it's highly likely that aircraft will come back and forward between the two.
As for the long term, I don't see EI flying to Australia and A340s are not in the game plan, unfortunately. However, they are looking at the far east and will probably be looking to feed into a oneworld hub at some stage - HKG or SIN. Australia offers a big potential market for Irish tourism and the Asia Pacific market is untapped, although the apparently imminent Emirates route should help to open this.