You can try LWP::Simple. if the server sets the content-type header correctly:

use LWP::Simple qw/ head /;
my ($content_type) = head($url);
[download]

without fetching at least the http header there's no way to determine the file type. If the file type is not set correctly you could fetch the body with LWP::Simple::get and then feed this to MIME::Types (after writing it to a file if necessary).

update: btw, your example url is simply html. but it has an iframe whose source links to a pdf.