Javascript is not magical.

After whatever Javascript has run, the browser still sends some bytes over the network to the webserver. All you have to do is find out what bytes need to be sent, and then send just these bytes via a Perl script. There is no magic, just plain hard work with Mozilla Live HTTP Headers and/or Wireshark.

Also see: On The Internet, Nobody Knows you're a Dog - the server only receives bytes and cannot distinguish between Perl and a Browser as long as both send the same data.