Just my personal opinion, but having many good friends in the US Army and many more x-military.
I find it inappropriate for someone (not in the military: enless you're married to one or kin to one) to wear a ring for any branch of the US Military, especially if you're not even in the states. Now if it was a POW/MIA ring, that would be better. Or look for a Aussie Military ring.
Im know if you tried you can find a site that can customize a ring for you, thats the same design as a class or "military" ring.
When I graduated from highschool we designed our own from a small book, send it to the company and they'd make it for us. We picked the metal, the gems, the signs on the side, and any wording on it. It just wont be as cheap as 19$. But sometimes its worth the it to pay out a little more.
But do whatever you want, I cant force you. Hope it all works out for you.