Well I think I have found the answer to my (and GPH's) question, and unfortunately it isn't the one we are looking for.
From the Qantas Chauffer Drive Ts and Cs:
5. Chauffeur Drive is also available in Adelaide, Sydney, Melbourne, Brisbane, Canberra, Hobart, Perth, Auckland, Christchurch and Wellington to passengers travelling on Qantas operated flights that connect to or from an eligible Qantas international flight above (and travelling in First or Business on the eligible international flight). Customers do not need to be travelling in Business on the domestic or trans-Tasman flight. The Domestic or trans-Tasman flight must be in the same booking as the eligible international flight.
Pity about that.