What is the average time taken to clear a customs checkpoint in Brisbane ?
I am (not an Australian citizen) flying in from the US in a flight that lands at 6.15 AM and have a connecting flight to Darwin at 8.30 AM. Would this be a sufficient time window ?
Sounds like you're on QF8 connecting to QF824 which means it's all on the one carrier - so worst case if there's a problem and you miss your flight Qantas will simply put you on a later flight to Darwin.
The standard "Minimum Connection Time" at Brisbane between those 2 flights is 2 hours, so you're within that window which means that a connection is at least possible.
Unfortunately Brisbane, like most Australian airports, has different Domestic and International terminals, located a few kilometers apart. Thankfully there is a landside bus which is free for connecting Qantas passengers which runs every 10-20 minutes so the connection is not difficult, but can take 30 minutes to get between terminals if you're unlucky.
QF8 is one of the first flights to arrive in the morning, and frequently arrives early, which means that there's normally not a large backup at immigration (especially as most of the passengers on QF8 continue on to Sydney without going through immigration).
So presuming your flight is relatively on-time (or early!) you should have no problems making your connection.