You're lucky this is one of my favorite general problems. :) Here is a functional proof of concept for you-

use warnings;
use strict;
use XML::LibXML;
use WWW::Mechanize;
use URI;

my $api = URI->new("https://product-search.api.cj.com/v2/product-searc
+h");

my %constants = ( "website-id" => "1594990" );

my $client = WWW::Mechanize->new( agent => "MyBot/0.0000001",
                                  autocheck => 0 );

my $api_call = $api->clone; # To make $api reusable without polluting 
+it.

$api_call->query_form( %constants,
                       keywords => "+sony -camera" );

$client->add_header(Authorization => "Some Nonsense Key 1234567890");

$client->get($api_call);

my $dom = XML::LibXML->new->parse_string($client->content);

print $dom->serialize(1);

__END__
<?xml version="1.0" encoding="UTF-8"?>
<cj-api>
  <error-message>Not Authenticated: Some Nonsense Key 1234567890</erro
+r-message>
</cj-api>
[download]