Another option is Stamp Auction Network where you have access to larger dealers that may or may not be better set up for international sales.
Here is an example of an upcoming auction from ModernStamps that may have a lot of what you need to fill those spaces.

If you find something you like, email the dealer (at least a few days ahead of the auction because they get busy near the end) to make sure they ship internationally and what they estimate the cost to ship a particular lot.
If you are not in a hurry, I agree with Parcelpostguy, search
ebay and filter by "Item Location - Australia only" to save on shipping (and possibly tariffs). Don't over-pay. Stamps in this period frequently sell for under USA face value. A collection of 1000 different 3 cent stamps will have a total "catalog value" of $250.00 but face value of just $30 which is closer to what you should pay for it.