For Thetravellingexperience, for a first timer, (trying to do T1 to T2/T3 in SYD), I would do it the other way around at least the first time, once, to learn the ins and out of it all, first, and then, later on, once you have done it, then you can do the T1 to T2/T3 within about 2.5 to 3 hours, till things settle down, dom security screening wise.
July is school holidays too.
So, maybe for this trip, try to do a transit via MEL, where you can easily walk between terminals, or
BNE, where there is the orange bus, and "probably" not so many people doing the transit, or doing the flight, and that you live in that city, so no rush.
IF QF hasn't done away with the T1 to T3 secure side bus, I would say, transit SYD.
But now that xray is done at T3 for QFd oncoming from T1, even 2.5 hours will be tight, not so bad if your flight from overseas is earlier on in the day, but would be scary if its later on in the day, or evening.
But QF SIN - SYD is early am, so even if you miss the SYD - BNE flight, there are other flights during the day.
Anyway, see if you can get the SIN - SYD flight changed, to avoid SYD.
