If you use a HERE doc, the quoted portion starts with the text on the next line. And all is well.

Using qq as you have (or "), you are including an initial newline character with nothing before it. This looks like an empty line to the mail program and makes it think you are already done with the header. But that "everything up to an empty line" header is empty!

So how about:

print MAIL qq|From: Me <me\@here.com>
  To: You <you\@there.com>
  Subject: Email

  body text|;
[download]

...or some such. HTH