You post is a little confusing
Are you looking for MEL-LAX? one way J reward on Qantas ?
Which airlines miles ? [Alaska?]

Mid to late Jan is the end of summer vacation for many here.
QF freq flyers will have booked 355 days out for this time
Many business's have 1-2-3 weeks with reduced staff - closed.
Many people tend to go back to work Jan 14, Jan 21 or Jan 28.
Schools start early Feb.

To me I would not have high expectations in mid Jan
Also try BNE - SYD to/from LAX- DFW