Firstly, well done on being in such a strong position.
I don't see any problem in getting a mortgage here. The banks major concern is that your application be as transparent as possible i.e. that they can see your salary, savings history, know your employer etc. You meet all these criteria.
They will want to see information on your spending pattern in Australia so they will look for bank statements from the last 6 months, at least. The fact that your spending is in another currency and that your income is subject to currency fluctuations might go against you.
You will be treated as an investor so the amount they will be willing to lend will be lower than if you were borrowing to buy your own home. Also, because of this, the interest rate charged on your borrowing will be higher.
Given that there are some complications with your application you might be better off applying via a mortgage broker.
The only question I have for you is why you are doing this? Have you done a business case for this? Does it stack up? The buying process here is alot of hassle. Letting one is even more hassle. Given your distance from Ireland both those issues are going to be more pronounced.
You seem to be in a strong financial position, do you really want to get into a complex deal like this?
If this is going to be a loss making exercise then I'd suggest you don't do it. Instead you could use your money to invest/save elsewhere and then stay in a very nice hotel when you come here. There are great hotel deals to be had here just now.
Anyway that's my tuppence worth, good luck with it.