I’d be looking to do a star alliance redemption on Air Canada personally, with AC starting flights direct from Melbourne to Vancouver shortly. The other option, of course, is United.
Unless you’d prefer to spend more time in the air (I wouldn’t) then flying the long way round to get to JFK via SIN & FRA.
AC would be MEL > LAX > EWR, and you’d be on a 787 for all segments.
UA would be MEL > YVR > EWR, and you’d be on a 787 for the MEL > YVR leg, then on something probably less nice (757 probably).
Both costs are identical in points, but I can’t help with extras (taxes, fuel surchage, etc).
Best bet is to search for availability on the UA site, and then call KF to ask about the costs and then make the booking.