It sort of does... for domestic flights:
Domestic premium services
Platinum, Gold, Silver Frequent Flyers, Qantas Club members and customers travelling in Business can check-in or drop off baggage at the Premium Service Desk when travelling on domestic flights.
The friendly, professional staff at our Premium Service Desks can arrange your international connections, help make changes to your journey and assist with any advice you may need.
and for international:
International premium services
First passengers and Platinum Frequent Flyers are able to check-in at the exclusive First check-in area at selected international airports, and fast-track through Immigration.
Business customers, Gold and Silver Frequent Flyers members, and
oneworld Rubys have access to dedicated Business check-in counters in all international ports.
Premium Economy passengers and Qantas Club members have access to dedicated check-in counters in selected international ports.