Assuming your theme or any plugin is not interfering with the generation of the needed HTML to display the logo, this should work.
1. Edit the qa-theme/<your-theme>/qa-theme.php file
2. Add (or merge, if it already exists) this function:
public function initialize()
{
$logoUrl = 'http://www.question2answer.org/images/question2answer-qa-logo-white-454x40.png'; // replace by the URL of your logo
$logoWidth = 40; // replace by the width of your logo
$logoHeight = 20; // replace by the height of your logo
if (qa_opt('logo_show') && qa_is_mobile_probably()) {
$this->content['logo'] = '<a href="' . qa_path_html('') . '" class="qa-logo-link" title="' . qa_html(qa_opt('site_title')) . '">' .
'<img src="' . qa_html(is_numeric(strpos($logoUrl, '://')) ? $logoUrl : qa_path_to_root() . $logoUrl) . '"' .
($logoWidth ? (' width="' . $logoWidth . '"') : '') . ($logoHeight ? (' height="' . $logoHeight . '"') : '') .
' border="0" alt="' . qa_html(qa_opt('site_title')) . '"/></a>';
}
}
3. You should only change the initial values of $logoUrl, $logoWidth and $logoHeight. Note they're equivalent to the options in section admin/layout. Leave the rest unchanged.