Here's a great deal for flights Down Under, travel Monday through Thursday from late September through late November, then again from the middle of January through March. Return flights in April are available so long as you depart by the end of March. A 7-night minimum stay is required, but that shouldn't be an issue as it would be crazy to fly all the way out there for anything shorter than a week.
Searching on United's website, I found seats departing MIA on Monday, February 18 and returning from SYD on Monday, February 25, 2019. A pleasant time as it heads into the tail end of summer in the southern hemisphere.
Looking for accommodation in Oz? Look no further, here's a full list of what's available for the sample dates via Hotelwatchdog.