Read the vBulletin API Basics how-to (https://vborg.vbsupport.ru/showthread.php?t=98009). It's telling you everything about creating your own custom vB page.
With the use of that tutorial, create a basic custom page with a template for the content.
Use the following code for the template:
$stylevar[htmldoctype]
<html dir="$stylevar[textdirection]" lang="$stylevar[languagecode]">
<head>
$headinclude
<title>$vboptions[bbtitle]</title>
</head>
<body>
$header
$navbar
<table class="tborder" cellpadding="$stylevar[cellpadding]" cellspacing="$stylevar[cellspacing]" border="0" width="100%"
align="center">
<tr>
<td class="tcat">Online Catalog</td>
</tr>
<tr>
<td class="alt1"><iframe src="http://www.yoursite.com/online-catalog/index.php"></iframe></td>
</tr>
</table>
$footer
</body>
</html>
The iframe tag is used to display a site (online catalog) in a site (custom vBulletin page). Ofcourse you need to change the iframe source link to the real url of your online catalog. More information about the iframe tag (adding a border to it, making it larger/smaller, ...) is avaiable here (http://www.w3schools.com/tags/tag_iframe.asp).