Unfortunately, there are no flights on QUantas from LAX-JFK. However, as an alternative, you might want to consider using QANTAS instead.

QF flights from SYD-JFK are usually quite full, so using 747's is well justified. I don't know how you can use QF for a flight originating from LAX to JFK since this has something to do with 5-th freedom rights which QF apparently don't have.

Nevertheless, if you manage to get a seat on this bird then you'll experience the luxury that no American carrier can offer you in any class (in comparison to the U.S. domestic product).