It appears you cannot use Exporting with https, because of "mixed active content" error.
Blocked loading mixed active content "http://export.highcharts.com/"
You can see this problem by viewing one of the Highmaps demos:
This (http) works: http://jsfiddle.net/gh/get/jquery/1.9.1/highslide-software/highcharts.com/tree/master/samples/maps/demo/distribution/
This (https) doesn't: https://jsfiddle.net/gh/get/jquery/1.9.1/highslide-software/highcharts.com/tree/master/samples/maps/demo/distribution/
Is there any way to allow Exporting to work with an https page?