I’d agree with BigDog on Ayres Rock. You could do a side trip from SYD to Ayres Rock, QF and APT do tours where you get the afternoon sunset over Ayres Rock and sunrise in the morning and a trip to the Olgars. Then on to Kings Canyon for a walk around the rim, then on to Alice Springs. That is one night in Ayres Rock, one night at Kings Canyon and then two nights in Alic Springs with a trip to the MacDonald Ranges and Stanley Chasm.
You could then fly down to MEL or back to SYD and then take the train to MEL which is a good trip and reasonably priced for first class.