With very rare exception, immigration in Australia occurs at your exit point from the country - in your case that would be SYD.
Australia has a clear distinction between "domestic" and "international" flights, as well as between domestic and international terminals (frequently separate physical terminals, but at a minimum separate sections of the same terminal). Specifically for both Sydney and Brisbane, the international terminal is a separate building to the domestic terminal.
Thus your BNE-SYD flight will depart from the domestic terminal in Brisbane, and arrive into the domestic terminal in Sydney. You will then need to get yourself (and possibly your luggage) to the international terminal. Depending on which airline(s) you are flying you may be able to catch a shuttle bus between terminals, or you may need to catch a public bus/train/taxi between terminals.
Once in the international terminal you will go to the check-in counter for your airline, then through immigration, security, and then to your gate.
In your specific case of Qantas connecting to United, the process depends on whether both flights are booked on the one ticket or not. If they are on the one ticket then Qantas in Brisbane will be able to check your bags all the way through to the US, and you will be able to catch the Qantas transfer bus which leaves from the Qantas terminal (near gate 2) and goes to the International terminal. If they are booked on separate tickets then Qantas will NOT check your bags through. You will need to collect them, make your own way to the international terminal, check-in, drop bags, immigration, security, and then to the gate. (If you don't have checked luggage you can still catch the Qantas bus)
In the first case, 1.5 hours is tight, but potentially doable if your flights are on time. United check-in closes 1 hour before your flight, so you've really got 30 minutes from your scheduled arrival until you need to be at the United check-in counter. At that time of day, the Qantas bus runs every 20 minutes. and takes close to 10 minutes. You do the math...
If you're on separate tickets, I'd go so far as to say you've got no chance if you have luggage.
I make this exact same connection at least once a year, normally more. Even as someone that's done it countless times before and knows exactly what I'm doing I would never book less than a 2 hour connection, and I normally do at least 2.5 hours to allow for delays/cancellations/etc. (eg, Qantas canceled my BNE-SYD about 2 years ago when connecting to United SYD-SFO)
