Your licence is valid for 5 years, but ratings attached to it are valid for a lesser period of time - SEP rating is 2 years.
LASORS will confirm this, but IIRC then you need training at the discretion of the CFI to pass a 'skills test'. This could be anything depending upon how 'rusty' you are. Again, IIRC, you shouldn't need to re-do any ground exams as your licence itself is valid.
Your local club CFI should be able to confirm this....just phone and ask.
As for OZ schools....yep, I'm sure there will be one not too far. But your ICAO licence should be recognized once valid again and you could easily convert it to an Aussie one if you're over there permanently.