I appreciate your concerns but I think you are worrying too much
Delays happen, and you will need to assess the impact in the day of travel. Assurances by the call centre are, at this stage, purely hypothetical, and you should be prepared for ‘self help’ as much as possible.
While the call centre says they will put you on the first available flight, what does that mean? First available Qantas code share flight? First available flight on another airline?
Unfortunately, while you were lucky in your Air New Zealand example, there are many many more examples where Qantas does not accommodate passengers on alternative airlines... 48 hour delays in Dubai and passengers were left stranded, not put on other carriers. Last year my friend had a cancelled flight from Hong Kong and Qantas only offered to reaccommodate on the same flight 24 hours later. It was only with my assistance that alternative flights were identified and we had to be in the front foot to get Qantas to actually effect that change (to MEL via BNE).
Qantas’ terms and conditions only state they will accommodate you on the next available Qantas service.
Waiting for QF to help can mean your options are severely limited. Of course if these delays happen in Singapore you’ll be fine... plenty of QF staff on the ground to help you. But in India you may need to be somewhat proactive.