I would consider taking it out of a ring case where it would be far more likely to be noticed. Put it is a gadget bag, pocket, etc. Then back into the ring case after customs.
I regularly travel with more that $900 in 'goods' Heck, I have 4 lenses each over that amount. A laptop. etc.
A ring mixed in with CF flash cards and other personal items would be my approach. As an alternative, put in in your toiletries bag. I just think a single ring, in a sea of clothing, would be more likely to elicit interest
Could even include a note: "Engagement Ring- Im proposing...dont blow it!"
... Its Australia, I bet it would work!