Firstly, thank you for reading this!

I just wondered whether anybody might be able to recommend what the fastest and most pain-free way of transiting Sydney airport would be, going from Terminal 1 to Terminal 3?

Basically, I'm in a rather fortunate position of having somehow managed to bag a 1st class redemption on Singapore Airlines in late December, arriving into SYD from SIN at 07:40am in Terminal 1. I then need to try and catch a 10:35am outbound flight (QF741; domestic; to ADL) in Qantas Business from Terminal 3.

Consequently, I just wondered what the speediest way of doing this transit would be? I've already been told that I will need to come through customs at T1, collect my luggage (from my inbound flight) and then make my way to T3, check in there and then clear customs again... all of which is totally fine, but I'm just curious as to what the most streamlined/time-efficient way to do this would be? It's just that I would only have 2 hours 55 minutes to make my connection (if things are running to schedule), which may well be ample, but not having done this before then I am mildly nervous having had a less than favourable experience of doing something similar at Perth airport before.

Any advice at all would be gratefully received!

Many thanks!