When you connect to the first URL the web server is sending back a few headers. The header indicating the redirection is the "Location". I ran

wget -O /dev/null -S 'http://images.imagefap.com/images/full/31/459/45
+9526477.jpg'
[download]

And note this part.

  HTTP/1.0 302 Found
  Connection: keep-alive
  Location: http://85.17.40.9:99/31a/full/459/459526477.jpg
  Content-Length: 0
  Date: Thu, 17 May 2007 05:11:56 GMT
  Server: lighttpd/1.4.11
[download]

With regards to how you can see that with WWW::Mechanize I don't know but the docs read

WWW::Mechanize is a proper subclass of LWP::UserAgent and you can also
+ use any of LWP::UserAgent's methods.
[download]

The docs for LWP:UserAgent indicate a HTTP::Response object is available and it's header() function might be what you are looking for.