It works great for me. I think that the problem is:

my($out,$err) = $ssh->cmd($cmd);
print "the output is $out\n"
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Hmmm...If you take a closer look at it, you'll see three mistakes. First, my($out,$err). $out and $err are being interpreted as filehandles here, and that's not what we want. Note that there isn't supposed to be a comma between $out and $err as filehandles. Also, you forgot $exit---without that, it won't work.

my ( $stdout, $stderr, $exit ) = $ssh->cmd($cmd); works better.

Second,  print "the output is $out\n";---$out is being interpreted as a global symbol, so you'll get warnings about needing an explicit package name. print $stdout, "\n"; eliminates that problem. Here's the complete script:

#!/usr/bin/perl

use strict;
use warnings;
use diagnostics;
use Net::SSH::Perl;

my $host     = 'host';
my $user     = 'user';
my $password = 'password';
my $cmd      = 'ls -l';

my $ssh = Net::SSH::Perl->new(
    $host,
    port     => 22,
    protocol => 2,
    debug    => 1
);
$ssh->login( $user, $password );

my ( $stdout, $stderr, $exit ) = $ssh->cmd($cmd);
print $stdout, "\n";
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Update: fixed typo