...and then be charged tariffs at the port of entry
I think that buy pre-owned in Singapore won't give you the tax-fee option that you have buying new
Do your homework and shop around in Australia but if you want to buy a new watch , I think Singapore will give you an advantage both on price in the shop and the fact that you can claim sale tax as a foreign national (make sure the shop does this!)
There is a thread on reddit precisely on buying a Seamaster tax free at Singapore airport
I am not sure it is ok to give the link so you look for it yourself.