LWP will follow the 301 so you will get the 200 from the new location. The details of the chain followed will be in previous. I have modified your code to get the Location from previous and it should do what you want. I have also added use strict and use warnings, as that is always sensible.

use strict;
use warnings;

use LWP::UserAgent;
use HTTP::Cookies;
use HTTP::Headers;

my $ua = LWP::UserAgent->new;
my $hh = HTTP::Headers->new(
  'User-Agents' => 'Mozilla/5.0 (Windows NT 5.1; rv:21.0) Gecko/201001
+01 
+Firefox/21.0',
  Accept => 'text/html,application/xhtml+xml,application/xml;q=0.9,*/*
+;q=0.8',
  'Accept-Language' => 'en-us,en;q=0.7,ru;q=0.3',
  'Accept-Encoding' => 'gzip, deflate',
  Connection => 'keep-alive',
);
$ua->default_headers( $hh );

my $cookie_jar = HTTP::Cookies->new( );
$ua->cookie_jar($cookie_jar);

my @rename = (
  294  ,
  9806 ,
  9807 ,
);

for my $ren (@rename) {
  my $res = $ua->get("http://www.giftman.ru/show.php?id=$ren");
  print $res->previous->header('Location')."\n";
}
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Output
/catalog/amulets/
/catalog/amulets/the_cult/
/catalog/amulets/aztek/
[download]