Hi Jeff,
There would be a very low probability of your June honeymoon being affected by cyclone activity, unless there was a very late category 5 cyclone in April-May.
In the mid '80s I went to Hook Island in the Whitsundays only 3 weeks after a category 2 cyclone went through. The only inconvenience was that the hot water system still wasn't operational. Also, a couple of years before that, I visited Fiji only a week after a Category 3 cyclone went through. It was almost as if nothing had happened. There were plenty of flattened buildings, trees and sugar cane but the locals weren't concerned at all. It was business as usual! Most people living in cyclone affected areas just pick themselves up, dust themselves off and get on with their lives.
The exception is when the more severe category 4 or monster category 5's hit but that isn't likely in the Whitsundays very late in the season.
Regards,
Geoff