I researched this flight quite abit in the last 15 odd minutes...
basically it only work Melbourne to LAX that way not other way round and it's cheaest tickets are on Monday, Wednessday and friday but the other days of the week still are around 501 all the tickets I've seen are between Mid october and mid november but there has been a lot more tickets than i expected
if you're searching for these tickets use Orbitz.com for whatever reason ITA software doesn't bring them up, Orbitz gives till next day 10PM Central to cancel