There is basically no chance of getting a flight from Sydney to New York in business class on Qantas in September. I had a quick look on their website and there are zero business seats. However, as you mentioned, you could possibly do a redemption on Cathay (via Hong Kong).
You can search for Cathay availability using Qantas’ website. Just use the multicity booking feature and break it up into SYD - HKG and HKG - JFK. The Qantas point calculator suggests it would be around 340,000 points return with about $900 in taxes/fees. Obviously this is a lot more than if you’d booked on Qantas (260,000 points return) but Qantas release very few seats on this route and they’re almost immediately taken. Availability actually looks really good at the moment in September on Cathay with about half the days having business availability, so book soon!
Of course, if you’re feeling a bit crazy you can also fly from Sydney - Dubai - JFK return on a mixture of Emirates/Qantas, but this will cost 400,000 points return.