Despite the press releases heaping praise on "a seamless "Virgin" experience," an interlining agreement really doesn't make the relationship between the rather disparate Virgin brands any closer. Most airlines have various interlining agreements; for example, United and American have an interlining agreement with each other, and V Australia and Delta announced one back in March. For the traveler, this usually means that you don't have to retrieve your luggage in the stop-over airport and check it in again for the next flight, as you would have to do if you were traveling on two airlines that didn't have an interlining agreement.
An interline agreement shouldn't be confused with a code-share agreement. That's when an airline can issue a flight number for a given flight, even if its code-share partner is actually the one operating it. (This is a common practice among airline alliance members. For example, US Airways flight 5947 between Spokane, WA and Denver is really operated by United Airlines flight 812.) Both airlines can then sell tickets on the same flight.
As of yet, there's been no announcement of any code-sharing between Virgin America and V Australia. But fellow 'Virgin' companies Virgin Atlantic and Virgin Blue already codeshare.