IIRC there are not any arrival lounges for TG in SYD. But, there are a few public pay per use showers in SYD. I think you'll need your own towel.
Edit:
http://www.sydneyairport.com.au/find...9C3855E5CD6%7d
In the pull down menu on the link it lists:
T1 (Before Customs/Landside) Near Check-in A & K
T1 (After Customs/Airside) Near Gates 21, 31 & 51