QF doesn't have arrivals lounges so unless your onward flight is on Qantas in business class ticket or you have Oneworld sapphire/emerald status you won't have access to the QF lounges in SYD.

As Voyager plat if you fly Air NZ from SYD you have access to the very nice NZ lounge, which has showers.

Assuming you don't have checked luggage or otherwise can through check bags then no need to clear immigration at SYD, just a security check to get to the departures area.

On a single ticket I'd want to allow 90 minutes to give a small buffer for delays and enough time for a quick shower. On separate tickets allow more time.

If flying Air NZ try to avoid the A320 operated flights - these have no business class and an uncomfortable economy class.

If flying Qantas watch for flights operating by their low-cost subsidiary Jetstar - avoid these.