After having experimented some, it looks like you cannot redeem gift vouchers for QBR flights. Further, the QBR member discount (even at level 1) offers up cheaper fares than are available via the gift voucher redemption search, at least for the flights I was looking at (JFK, LHR). While you don't pay credit card fees on gift voucher bookings, the QBR "member" fare works out a bit cheaper than the gift voucher fare even with the credit card fee included.
So it appears you save money booking via Qantas Business Rewards, at least for the international flights I was looking at. But the question remains: Do you get personal DSCs if you book Qantas Business Rewards fares? Does anyone know?