How to allow arbitrary query string with url alias?
Drupal doesn't treat the query string as part of the URL alias, the problem is that your URL has the q parameter as part of it (q=dom).

Google obviously uses that for some purpose, but Drupal uses $_GET['q'] to determine the path of the page that should be shown. So when you visit a URL with q=dom in the query string, Drupal will try to find a page with the path dom...which obviously doesn't exist on your server.

Short of some crazy hacking of Drupal core (and probably dozens of contrib modules) I think the only way you're going to solve this is by somehow changing the original query string and removing the q parameter from it.