To preselect an item if the page is within the active trail, apply the following modifications to quickmenu.module.

Find the following line in function quickmenu_block (case 'view'):
$block_content .= '<option value="' . $the_link . '">' . $qm_full_menu['items'][$child_mid]['title'] . "</option>\n";

and replace it with the following lines:

$selected = menu_in_active_trail($child_mid) ? ' selected' : '';
$block_content .= '<option value="' . $the_link . '"'.$selected.'>' . $qm_full_menu['items'][$child_mid]['title'] . "</option>\n";