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 earn Skywards Miles on Qantas-operated flights?
Can I earn Tier Miles on flights operated by Qantas?
Can I earn Miles on domestic travel within Australia?