Not certain how to do this, but may be able to give you a few hints. Internet Explorer has, I believe, got an OLE interface which can be linked with any scripting language- including Perl. Assuming this OLE interface allows you to do the 'Print to file' command scripted then you should be able to grab the output and throw a basic regexp at it to pull out the page count.

I have had a quick look at the MS website, but couldn't find the documentation on IE's OLE interface. I suspect you should be able to find it at a website dedicated to a Win32 specific-language such as Visual Basic or somesuch though.