If your bags are checked through, (OR not in the most possible case), you will find that even thought its the same terminal, ie, SYD international terminal 1, due to the fact you have to get through Aust Customs and/Quarantine, it will be a very lot of walking.
No fun.
Even coming back from NZ to Au via SYD for me, does mean a lot of walking.
No travellators from the arrivals gate to the Border Force hall, left and right hand turns, (not like SIN Changi), ...
I would change a flight, but thats me, change the INC - SYD one to the day before if at all possible.
If same tix (same PNR)/same alliance (which its not in your case), I don't like your chances.
Even if its 30 mins from plane getting to gate, you have to walk from gate to hall, then take a few mins to slip your passport into Smartgate reader, few mins to wait for the bright lights, then collect bags, then to go to green channel, and maybe get chatted to, maybe not, then face the scrum of people meeting friends/relatives, go upstairs to international departures, wait in line to check in, rush through international outwards immigration...
Best of luck anyways.