UK expat based here in Singapore... so not too far away from you in Oz.
I've had no trouble obtaining small quantities from Mouser for all my projects over the years. In fact, I took delivery just this week of a small quantity for restoration of my Tektronix scope.
The only thing you "may" need to be aware of is their shipping cost threshold. Above a certain (total) order cost threshold, shipping is free... below that threshold, you have to pay shipping etc.
Ordering via Mouser Singapore, the components are still shipped from the US.
I think Digikey, RS, and Element 14 all do the same, as all four are competing against each other for one's business !