Are you saying that an Aussie type rating is "LHS or RHS" valid only?
Potentially, yes. For multi-crew aircraft you can attain either a 'command' (allowing you to fly LHS and RHS) or 'co-pilot' (RHS only) type endorsement. Also there are command and co-pilot versions of an instrument rating too.
However, once CASR Part 61 takes effect on the 4th of December it seems they intend to not have co-pilot qualifications any more. Makes sense to me. The worst case scenario would be a co-pilot having to take over if the captain is incapacitated. Seems to me you'd want the guy in the other seat to be equally well trained and qualified to fly it!