catfile, like you are already doing for the source directory.

use strict;
use warnings; 

use File::Copy            qw( move ); 
use File::Spec::Functions qw( catfile ); 

my $src_dir = 'F:\\test'; 
my $dst_dir = 'F:\\oldbackups'; 

opendir(my $dh, $src_dir)
   or die("Can't open directory \"$src_dir\": $!\n"); 

my @dirs; 
while (defined(my $fn = readdir($dh))) {
   next if $fn eq '.' || $fn eq '..'; 
   my $src_qfn = catfile($src_dir, $fn); 
   next if !(-d $src_qfn && -M $src_qfn > 0);
   my $dst_qfn = catfile($dst_dir, $fn); 
   move($src_qfn, $dst_qfn)
      or die("Can't move directory \"$src_qfn\" to \"$dst_qfn\": $!\n"
+); 
}
[download]