Business class and even premium economy awards are pretty scarce on flights to the US from Aus. BUT there are a few options.
You can transfer to Velocity at a 4:3 ratio. You can redeem for Virgin Australia’s flights to LAX from melbourne, sydney or brisbane. You can also redeem Delta Airlines flight to LAX from Sydney. Business class on both Virgin Australia and Delta will cost 95500 Velocity (128,000 Gateway points) and premium economy (only on Virgin) is 71700 Velocity (95,600 Gateway). I’d recommend searching all 3 cities above to see what you can get and buy a domestic flight to the other cities if not departing from melbourne.
Same transfer rate at 4:3 and you can redeem for Singapore Airlines, Air Canada, United Airlines and even Air New Zealand. You can redeem Singapore Airlines from Melbourne, Sydney, Brisbane to New York, LA, Newark, San Francisco, Houston and soon Seattle. You’ll need 121,000 for business class flights to the west coast. Partners like Air Canada and United will cost a bit more with Air New Zealand being near impossible as they never release business awards. Keep in mind if booking SIngapore Airlines awards, you can hold the award and transfer so that business class award doesn’t dissapear.
This is the program to transfer to for travel on Qantas and other OneWorld airlines like American and Cathay Pacific. You’ll need 90000 asia miles for business class Qantas flight from MEL - LAX or you could consider Syd or BNE to LAX if availability are scarce. The same rate applies to American Airlines’s SYD to LAX route. Cathay Pacific Business will cost 115000.
HOPE I’ve given you some options to consider. Given this is a pretty competitive route for premium cabin awards, I would search all the options below for possible award availability and different city pairs as well.