No, currently there is nothing like that available.
Currently you can take a screnshot afaik.
I'd love ZOs to implement something like that QR code into the console error UI themselves but actually they would need you to send it anywhere then: like the QR code only would show a link, but what should the link open then?
There would be the need for a website where the link redirects to AND includes the error message, and you'd need a possibility to share it with the developers too.
I cannot think of any easy way to do that. You'd need a database, usernames, access etc.
And the QR code generated alone would maybe work if there isn't too much text in the error messages. But as error messages are pretty long I doubt you can put all of that into 1 QR code (or it will get pretty big on screen).
And even then you'd have to share that as a screenshot properly in the end, so putting screenshots of the different error pages might be similar (for the moment).
While consoles are limited to a screenshot solution, perhaps an addon to replace the UI window that displays the error. With a better contrast between text and background. And if the author is feeling generous.. toss in some syntax highlighting and the ability to scroll up if it excedes the boundaries of the window.