The northern Queensland coast, between Cairns and Townsville is likely to see 25 to 50 mm rain over the course of just a day or two, with local falls ranging from 50 to 75 mm.
Most of this is likely to fall on Tuesday.
That's the average rainfall over the entire month of June for much of this area.
The rain is likely to not just brush the coast, but spread well inland, with lighter rain extending right down to Bundaberg too:

The area just inland from Cairns usually sees only 5 to 10 mm in this month - as part of the dry season - so these rainfalls could be five times what they usually see in a month, in just a day or two.
The cold outbreak that arrived in the southeast last week, that spread frost into southern Queensland, is also driving this weather system. In order to get rain you need moisture and low pressure to work together. This outbreak comes with an upper atmosphere trough, and that instability is working with the moisture from onshore winds to create this out of season rain.
The rain comes with cloud .. and that is spreading right down into the southeast. So, while the rain won't reach the southern inland, the cloud from it will, easing the frosty conditions.
