Always hard to advise on how long to book your connection for in SYD, but 1.5 is the absolute minimum, and 2 hours should be ok. The only issue is if the NZ flight comes in late or the customs queues are horrendous. Qantas should be able to help if you misconnect, but aren't required to as you will be on seperate tickets.

NZ won't be able to check your bags through. In SYD (unless catching a QF flight numbered 1-399) you are required to clear immigration and customs, and collect your bag. You then go to the "Domestic Connections" area, recheck your bag and take the bus across to the domestic terminal. You are allowed to use the bus service because you will then be flying Qantas. Much less hassle than using the train or other connecting busses.

If your QF flight is numbered 1-399 then it's a totally different game, and I believe NZ can interline bags with Qantas to MEL. You would then clear customs in MEL. However, the only 1-399 flight in the morning is less than the minimum connection time needed in SYD (IIRC, 1 hour international-international and 90 mins dometic-intl // intl-domestic)

763's are more comfy (plus the twin aisle helps), However both 763's and 734's in the Qantas fleet are showing their age.