The website indeed is inconclusive.
http://www.qantas.com.au/travel/airl...eles/global/en
Given TBIT's structure with separate arrivals and departures, you may need to go landside.
http://www.qantas.com.au/travel/airl...oom-1111/am/en
Inter-terminal Transfers
Qantas passengers arriving at LAX Terminal 4, ... bus ...
For other connections, an inter-terminal bus provides free transportation between all LAX terminals on a regular basis, which can be accessed from the center island on the Arrivals level from all terminals.
This should not be much of an issue as it's a 100 yard walk and T4 security is normally very quiet this time of the evening.