A choice you might look at is going to Skyscanner and selecting the whole month.. from anywhere in the USA to anywhere in Australia. You need to select the whole month option.
This will give you some choices… from there you can narrow down your dates, departure and arrival cities.
You may find that it is cheaper to fly out of one city and back to another, likewise to one city, and out of another on your return flight. And check for one ways in each direction. Then test the prices on a real website (not a meta engine) like Future.Travel.
Best to do your shopping now… Given your stated budget a quick look on the Future.Travel website shows you can have a very Merry Christmas in Australia with about A$1000 left for shopping for last minute gifts.
Hope you can help spread the seasons meaning by purchasing online with Future.Travel where we automatically donate the dollars of our transactions to help those in need. Check out our CSR programme for online purchases: Corporate and Social Responsibility and Serving children in Vietnam with a focus on education