QF can use the plane from MEL (QF93) or 149 from SYD (if operating that day and is a 3 class aircraft) to continue to JFK and may do this even if 107 is on time from personal observation. If you are late into LAX and connecting then QF will rebook you automatically onto another flight and on arrival in the baggage reclaim area in LAX QF groundstaff will hand you a new boarding pass and instructions. This flight could be operated by any carrier (not just AA) and you will then need to fax QF to get the points if it is not an AA flight.
Personally I wouldn't worry about this, it is not a big issue.