This is not working
Your code starts with Use REST::Client; when it should be use REST::Client; because Perl is case-sensitive and use needs to be all lowercase. It's no surprise it isn't working.
You may also need to set some headers depending on what the server expects. Here is a fully working SSCCE to get you started.
#!/usr/bin/env perl
use strict;
use warnings;
use REST::Client;
my $rest = REST::Client->new ({
host => 'http://httpbin.org'
});
my $data = '{"key":"value"}';
my $headers = {
Accept => 'application/json',
'Content-type' => 'application/json',
};
$rest->POST ('/anything', $data, $headers);
print $rest->responseContent;