Upvote:4
You're not the first to wonder, and there are already websites set up for such plans!
RVWorldWide has an exchange/swap program, and indeed there are Aussie and American listings on there. It would be worth a post.
MotorhomeHolidaySwap is growing, it only has 1700 members, but these are actively trying to swap for holidays around the world, so does sound exactly like what you're looking for.