This is the right direction, but over-complicates it a little. Unless you need different text or the image is a different size, there is no need to duplicate the information in the header.php file and you could simply create the new file and use the following code snippet instead (i.e. no CSS additions)
PHP Code:
<?php $logo_image = $this_is_home_page ? HEADER_LOGO2_IMAGE : HEADER_LOGO_IMAGE; ?>
<div id="logoWrapper">
<div id="logo"><?php echo '<a href="' . HTTP_SERVER . DIR_WS_CATALOG . '">' . zen_image($template->get_template_dir($logo_image, DIR_WS_TEMPLATE, $current_page_base,'images'). '/' . $logo_image, HEADER_ALT_TEXT) . '</a>'; ?></div>