Fares are based on seasonality, then vary depending on how far ahead you book, on the type of promotiional ticket e.g 21, 15, or 7 day advance; or ones saying immediate payment required.
Airlines also vary greatly in price, and it can depend on which route e.g I've found JAL the cheapest for Melbourne to New York, flying via Tokyo. So, it may depend if you don't mind which airline, having a longer journey, and transiting, to save on cost.
Let your travel agent know these things.
Book early as Christmas is a peak season. Last minute bookings are dearer. One way fares are expensive, so check the cost of a return, it may be cheaper if there is a deal on,(sounds crazy, but believe me it can happen)
You don't have much time, so seriously start looking. 