Hi, Taran.
I can’t think of any reason why this would fail just in IE9. Are you quite sure that you are not using IE in its infamous “compatibility” mode?
You might try updating the version of jQuery that the theme uses. You can get the latest version of the script from http://jquery.com/
The jquery-1.8.1.min.js file can be saved to the same location as the current version – wp-content/themes/theme-traject/js/ – then you can update the reference in the header.php file by replacing this reference:
wp_register_script('jquery', ($themePath ."js/jquery-1.4.2.min.js"), false, '1.4.2');
With the new one:
wp_register_script('jquery', ($themePath ."js/jquery-1.8.1.min.js"), false, '1.8.1');
It’s worth a try. Other than that, I’m clueless. On my iMac your form works properly across all major browsers, and even a couple of minor ones. You might try opening your JavaScript console in IE to see if any errors are being generated. I’ll run it past @andy to see if he has any ideas.