While this may be a good exercise in directory traversal, i'm wondering what would be wrong with  cp -r $src_dir $dest_dir.

If you really want to do it in Perl, you might find File::Find helpful. I noticed that you have a comment saying #recursively search  $path for files, but your code doesn't recurse into subdirectories at all :) GrandFather already pointed this out

Another minor detail is that you're not distinguishing between files and directories, and I'm pretty sure that File::Copy's copy function doesn't handle copying directories.