The fonts might be a problem if you needed to keep the materials in Quark, but you don't; they're going to the web, where they'll most likely end up as default web fonts. So even if all the fonts default when you use Quark on the PC to open the Mac Quark file, you can still "select all" to grab all the text, then paste it into Dreamweaver (or whatever web application).
So I would think all you need is to have Quark on the PC.
What you probably WILL have trouble with is losing all your text formatting when getting text from Quark to the web. Someone may have an idea of a good workflow for this.