Unfortunately, right now LiveReload browser extension cannot access file: URLs in Safari. This is a security limitation of Safari extensions API. (I hear that the limitation has been lifted in Yosemite, but I couldn't find any documentation on that, and couldn't get it to work. If you know the details, please contact me!)
You either have to use the <script> snippet (instead of the browser extension), or use a local web server to serve your file over an http: URL. Please contact me if you need help.