If I am already a Qantas Frequent Flyer, can I earn Qantas Frequent Flyer points in addition to my Emirates Skywards Miles?

No. You can only earn either Emirates Skywards Miles or Qantas Frequent Flyer points per flight. The benefits you will receive will be as per the Frequent Flyer number quoted in the booking.

Related questions

Can I use the Miles Calculator to work out how many Miles I can earn on domestic flights?
Why is a fare not quoted when I search using ‘Timetables’?
How do I use the ‘Timetables’ feature?