Sure, but that's not as fun as the, uh, "organic" connection you can make over radio.
(Earth-Moon-Earth communication, or moonbounce, is basically to aim your antennas at the Moon and blast as much RF as you can muster at it, in the hopes that someone will pick up your echoes as the arrive back at Earth 2.5 seconds later.)
Anyone having the Moon over their horizon at the same time as Australia does should have a fair shot at working an Aussie at 144MHz and above.