Hi! What is your price range? I am also in Australia and am just about to put a Mya Moe tenor on the marketplace...shipping would only be around $35 and take a couple of days...but it is an expensive uke $1000+... :uhoh:
I'm looking for something under 500 at the moment. If I had a grand John, I'd buy that uke in a heartbeat.
I've found some nice ukuleles online, however none so far have been able to send to Australia.
Have you looked at Hawaiian Music Supply - http://www.theukulelesite.com. they offer a good service, setup and ship to Australia. i've previously bought a Kamaka concert from them in the past with no issues. The Kamaka's higher than your price range but they have others below the 500 mark