What I don't understand is why the OP is booked on such a circuitous route (SYD-MEL-SIN-DXB).

Were all the SYD-DXB and SYD-SIN-DXB on that date full in F?

If the OP is just going via MEL for the hell of it...well, then, I don't see why a second car would really be due in SYD at all. If the SYD-MEL was on a separate day from all other journeys, then of course none of us would say that a car was due. If the OP decided not to see MEL and, therefore, NOT to take advantage of the opportunity to use the car that was due in MEL, then I think that's on the OP.

Perhaps you can enquire about cutting out the unnecessary SYD-MEL detour and fly back from SYD directly?