A while back, I had to write a script that crawled a site which distributed a file through a flash application. I noticed that the cookie was always contained in the url and followed a specific pattern. Thanks to PerlMonks, I was able to figure that out. Firstly, I used WWW::Mechanize::Firefox.. you may need to in this case, too- I'm not sure. Anyways I start with something like:

use strict;
use warnings;
use WWW::Mechanize::Firefox;
use Data::Dumper;
use DateTime; 
## you can set the date to nearly anything with this module, refer to 
+its documentation

my $mech = WWW::Mechanize::Firefox->new(launch => 
'C:\path\to\your\firefox.exe', 
autoclose => 1, autodie => 1 );

my $jar = $mech->cookies();

print Dumper($jar); # for debugging, you need to understand the data s
+tructure of this cookie to properly use it
[download]

Alternatively, you may not need to use the cookies at all. But since it is not completely clear to me what your goal is with this script, I can't say for certain. Briefly looking at your url, you may be able to use just plain old WWW::Mechanize and then $mech->dump_text;