I believe the empty tree is put there so the extracting software can extract it to exactly where it came from. That is, when extracting the program can create C:...carl. I suggest something like:

my $dir = 'C:\Windows\Desktop\carl\zip\mysql';
my $file = 'C:\Windows\Desktop\carl\test.zip';
my $name = 'backup';

my $zip = Archive::Zip->new();
chdir $dir;
$zip->addTree( ".", $name ) == AZ_OK
  or die("could not add tree");

$zip->writeToFileNamed( $file ) == AZ_OK
  or die("could not write file");
[download]

HTH, --traveler