I am thinking it really depends on the policies of Qantas at LAX.
Interestingly the web site has no specific indication of check-in being available for QF107 at all!
http://www.qantas.com.au/travel/airl...Guide | Qantas
The closest reference is this part:
Originally Posted by Departure Information
Ticket Counter
Ticket counter is located in the centre aisle (aisle B) of the Tom Bradley International Terminal.
Opens at 6:30am and open till 9am for the QF107 departure to JFK. No check-in, baggage acceptance or ticketing functions until 4pm. Early check-in counters open from 4pm. ...