Don't forget to use strictures:

use strict;
use warnings;
[download]

You can see what the handshake is doing by using IO::Socket::SSL.

#!/usr/bin/perl

use strict;
use warnings;
use IO::Socket::SSL qw(debug3);

require LWP::UserAgent;
require HTTP::Request;

my $ua = LWP::UserAgent->new;
$ua->agent(
    "Mozilla/5.0 (Windows NT 6.1; rv:29.0) Gecko/20100101 Firefox/29.0
+");
$ua->timeout(10);
$ua->protocols_allowed(['https']);

my $req = new HTTP::Request 'GET' =>
    'https://tutorialregistration.uws.edu.au/aplus/admin/adminLogin.do
+';
$req->header(
    'Accept' =>
        'text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0
+.8',
    'Accept-Language' => 'en-US,en;q=0.5',
    'Accept-Encoding' => 'gzip, deflate',
    'Cookie'          => '',
    'Referer'         => 'https://www.uws.edu.au/',
    'Connection'      => 'keep-alive',
);

my $res = $ua->request($req);
print "content-type:text/html\n\n";
print $res->content;
[download]