From the Qantas FF Handbook:
10. Redeeming Points
10.1 General
10.1.1 Awards are subject to capacity controls and availability is limited. Qantas, oneworld Alliance Airlines, Frequent Flyer Partner Airlines and Frequent Flyer Partner Services limit the number of seats/rooms/vehicles and other products or services available to Members at their absolute discretion. These depend on the flight, date, season and destination and some flights may not have any Awards seats available. Once Award seats are filled there may be no more Award seats available. Seats for Award travel are booked in special classes of service. If the class of service applicable to the Award is not available, another flight, date or destination must be selected. You must not reserve a seat in an incorrect class of service.
10.1.2 Members will be personally liable for any and all costs, taxes, charges, claims or liabilities of whatever nature (including without limitation all ticket taxes) arising from the provision or availability of any Awards or Benefits whether these are provided by Qantas, a oneworldTM Alliance Airline or by a Frequent Flyer Partner Airline or Frequent Flyer Partner Service.
10.1.3 It is the responsibility of each Member to keep track of any and all redemptions made against their account and ensure that sufficient Points are held in credit to cover any unticketed Award Flights or services. Members must report any unauthorised Award claims from their account within 12 months of the occurrence. Corrective action cannot be taken after that time.
10.1.4 You may assign any Award you earn through Qantas Frequent Flyer to any member of your family covered in the list below. However, there may be tax implications on such a transfer for Australian taxpayers and you will need to consider clause 10.1.5 below. Your eligible family members may use the Award whether you travel with them or not. Award tickets issued for a member of your family must be in the name of the passenger travelling.
Husband/Wife
Parents/Step-parents
Domestic Partner/Defacto
Children, includes foster and step-children
Brothers/Sisters
Half Brothers/Sisters
Grandparents
Grandchildren
Sons/Daughters-in-law
Brothers/Sisters-in-law
Fathers/Mothers-in-law
Uncles/Aunts
Nephew/Nieces
First Cousins
Now, having said that, why don't you join your girlfriend to QF FF, using your address as hers (thus seen as domestic partners). I never had any problem using points for my girlfriend, later fiancee, now wife.