If I break lease before an upcoming rent increase, does that give them an op to revise it?

Hey, long time listener, first time caller. As per the subject, with a bit of luck I've secured a house to replace my overpriced unit located right next door to a poorly managed social housing complex in north Brisbane. We've had an increasing array of issues over the years, with the final straw being a threat at my front door.

Anywho, I have a scheduled rent increase on 2 December. I have already signed and paid for the new place and we move in on Jan 3. We are breaking the unit lease very early (however I have lived here for seven years) and it occurs to me that if I give them notice before 2 December, they might have an opportunity to "update" and change the once-per-year increase in light of my upcoming exit.

It was a bit hard to find this clarification online but basically - can they do that? Should I just issue the Notice of Intent to Leave ASAP, or wait until 3 December to ensure my agent gets fucked over? I know I'll be paying reletting fees either way and have budgeted for that.

The agency managing my unit have been extremely unhelpful. They stalled so badly on providing a rental reference for the new place that our application originally wasn't even put up for consideration at all for the owner. It was the best place we've seen all year, and I was absolutely furious that the agency cost us the opp. This happened despite an email exchange about the security issue, and despite the fact I've never been late on rent in seven years.

We were only successful in a second chance draw (successful applicant pulled out and the agent threw us a bone) - basically used up my year's worth of luck right there.