Are you interested in what Firefox sends, or in what you receive back from the HTTP server?
If the latter there are many Perl modules that will capture those, for example
- LWP::Simple has head($url) returning ($content_type, $document_length, $modified_time, $expires, $server)
- WWW::Mechanize has $mech->dump_headers( [$fh] ) which will print all the response headers to the given filehandle or STDOUT.