1. Check File::Copy to do the copying of a single file.
2. Write a recursive function that, if it bumps into a file, copy it, if it's a directory, create the new dest directory and copy stuff into it.

something ala.. (untested! gotta go to work!)

Update: Woops.. thought you wnated to copy directories, not single files. Morning eyes.
Update 2: Retitled to something more appropos..

use File::Copy;
sub rCopy
{
    my $src = shift;
    my $dest = shift;
    if( -f $src )
    {
        copy $src, $dest;
    }
    else if( -d $src )
    {
        mkdir $src . "/" . $dest;
        my $dh = undef;
        opendir( $dh, $src );
        while( my $rSrc = <$dh> )
        {
            rCopy $rSrc, $src . "/" . $dest;
        }
    }
}
[download]