Rather than using a lookup hash, you could build a sort order hash and use a Schwartzian Transform to sort into the new array. I have changed the desired order to illustrate the %sortOrder hash more clearly.

use strict;
use warnings;

use Data::Dumper;

my $raUserOrder = [ 5, 1, 4, 3, 2 ];
my %sortOrder   = do
   {
       my $count = 0;
       map { $_ => ++ $count } @$raUserOrder;
   };

my $raQueryResults  = [
   { key => 4, name => q{label4} },
   { key => 2, name => q{label2} },
   { key => 5, name => q{label5} },
   { key => 1, name => q{label1} },
   { key => 3, name => q{label3} },
   ];

my $raSortedQueries = [
   map  { $_->[0] }
   sort { $sortOrder{$a->[1]} <=> $sortOrder{$b->[1]} }
   map  { [ $_, $_->{key} ] }
   @$raQueryResults
   ];

print Data::Dumper->Dumpxs(
   [ \%sortOrder, $raSortedQueries ],
   [ qw{ *sortOrder raSortedQueries } ]
   );
[download]

Here's the output.

%sortOrder = (
               '4' => 3,
               '1' => 2,
               '3' => 4,
               '2' => 5,
               '5' => 1
             );
$raSortedQueries = [
                     {
                       'name' => 'label5',
                       'key' => 5
                     },
                     {
                       'name' => 'label1',
                       'key' => 1
                     },
                     {
                       'name' => 'label4',
                       'key' => 4
                     },
                     {
                       'name' => 'label3',
                       'key' => 3
                     },
                     {
                       'name' => 'label2',
                       'key' => 2
                     }
                   ];
[download]

I hope this is of interest.

Cheers,

JohnGG

Update: Corrected typo.