Evening
Gary,
Qantas' BNE/LAX/BNE services are operated by a mixture of 747-400s. Incidentally, VH-OEJ "Wunala Dreaming" operated QF0015 yesterday. Generally, most flights are operated by the 2-class 747-400s, however in recent times, aircraft offering First and Premium Economy have been utilised.
With regards to your flights, planned configurations are as follows (subject to change):
18MAR QF0015 BNE/LAX: 4 Class 747-400 (52J with Premium Economy)
22MAR QF0016 LAX/BNE: 4 Class 747-400 (52J with Premium Economy)
Seatmap -
http://www.qantas.com.au/infodetail/flying/inTheAir/ourAircraft/744-14P52J32PY255Y.pdf
AFAIK, first 2 Class 747-400 with Premium Economy will commence services in May (BNE/LAX/BNE PE fares should be available for sale in the coming months).
Hope that helps,
Cheers