The docs don't seem to state it, but you can actually pass in a filehandle instead of a local filename. However, it appears you then *must* specify the remote file name.

my $ftp = Net::FTP->new("ftp.example.com");
$ftp->login('username', 'password');
$ftp->binary();

while (read INFILE, my $data, 2000000)
{
    open my $datafh, '<', \$data;
    $ftp->append($datafh, $fileToWrite);
    # Here's where I will print the progress...
}

$ftp->quit();
[download]

Or something like that. (UNTESTED) Good luck :-)