As someone that was a long term student (6 years) and college resident at said University, I agree your best bet is to limit brew club membership to +18 students. That way you shouldn't have too much opposition from the student union or the Uni itself. Whatever your members decide to do with the wort is their business.
I doubt youll have much problem holding brew days on campus, however your problem is going to be when someone wants to drink.
From memory (a very hazy one at that) when I was a resident at one of the colleges, the official stance was there was to be no alcohol outside the licensed areas and functions (This was late nineties, so not sure what the latest stance may be) In saying that, the college wardens, security and staff never really gave a rats arse if you were having piss up in your rooms as long as you were reasonably quiet and didnt annoy anyone.
So, even though an eye may be turned when youre doing tasting sessions on campus, your best bet is to organise a calender of events and hold them in the official licensed venues... no idea what this means as for bringing your own. You may want to talk to the UQ Wine Appreciation Society and see how they overcome such things. Or of course do them off campus.
Also, if you can talk to any of the other clubs/societies that hold functions involving alcohol for how they handle things. SECS is the one that jumps to mind. Their sport day is an experience that haunts me to this day (some things just cant be unseen)
I can already see how someone were to setup their own fermentation and serving fridges, by way of 2 bar fridges in the corner at the end of the bed in the colleges. In saying that, approach the colleges, perhaps the student social convenors. Let them know that they can produce their own. I know some guys in my day were doing KnK in the rooms and fermenting in a shared space. No reason you couldnt get them to setup with a BIAB setup and a group kegerator to supply the student executive as an example
Anyway good luck with it, hope it gets up. Id be keen to come along to one of the brew days in the future.