In order to preserve your order you may want to do something like this:

$cat[0] = ["birds",
           ["Sub array listing 0.1.0",
            "Sub array listing 0.1.1",
           ]];
$cat[1] = ["turds",
           ["Sub array listing 1.1.0",
            "Sub array listing 1.1.1",
           ]];
foreach my $elem ( @cat ){
  my $name = $elem->[0];
  print "My name is \"$name\"\n";
  foreach my $sub_elem ( @{ $elem->[1] } ){
    print "My Property is: $sub_elem\n";    
  }
}
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my @a=qw(random brilliant braindead); print $a[rand(@a)];