You can use the path in your call to get. Replace your call to get with this one.

$ftpBox->get("$remotedir/$filename","$destination_dir/$filename") 
 or die "failed to get $filename to $destination_file";
[download]

If your just interested in checking to see if a directory exists. Then an ls or dir is almost as good as cd.

$ftpBox->ls($remotedir);
#or 
$ftpBox->dir($remotedir);
[download]

Updated: Added a little more info.