If you use <code> tags your quine becomes much simpler:
my $ua = LWP::UserAgent::new ('LWP::UserAgent');
LWP::UserAgent::agent ($ua, 'Mozilla/5.0');
my $url = "http://www.perlmonks.org/?displaytype=displaycode;node_id=6
my $request = HTTP::Request::new ('HTTP::Request', GET => $url);
my $response = LWP::UserAgent::request ($ua, $request);
Also, you don't break formatting for replies to your node.
Edit: I think you want a question mark after dot-star. Otherwise it's q-positively trivial for me to break your code.
I just realized that, if you put a question mark after dot-star, the end of your regex matches itself. But there are ways around that.