I think you'll need to talk to a solicitor in Ireland. Usually, AFAIK, the tax owing on the inheritance is calculated on the value of the inheritance at the point of taking ownership.. if the value changes between that date, and the date it gets sold, you may have to pay cap gains on the difference as well. I suspect residency won't make any difference to the tax free bit.
I don't think the Australia bit is (for what you're asking) relevant; it's all about how Ireland works. That's how it sounds.
But yeah. Surely the executor of the will and the solicitor will deal with all this *before* any money gets passed on..?