For those that know, for the most part, the only outlets for AB to play shows in Australia/New Zealand was through being an opening band, as they did when they opened for Disturbed and P.O.D. back in 2008, I believe, or through the Soundwave Festival (which they did back in 2012 and 2014). However, the Soundwave Festival was no more due to a multitude of poor booking/logistic issues in certain cities/low attendance/bands weren't getting paid in past festivals/etc. Therefore, it was unknown whether or not AB would find their way back to the land down under.
However, they just announced that they would be doing a small headlining tour in Australia/New Zealand in April. Here are the tour dates.
http://mjrpresents.com/alterbridge/
I imagine tickets would cost at least twice as much as the typical US GA price since playing there is expensive, but since AB managed to book a couple of shows there, I imagine it would sell well enough at the price that is set.