I have never used URI::URL but from the code you linked to, it appears that you would do something like this:

$url = new URI::URL $links, $content->base();
print LINKS $url->as_string(), "\n";
[download]

I think that should work, but it hasn't been tested. You may be able to use print LINKS "$url\n"; but I can't tell from the documentation if it is the same thing.