As someone once said, "You can program C in any language."

Here is a more Perl-ish solution:

#!/usr/bin/perl -w

use strict;
use warnings 'all';

my @arr = ( 1, 2, 3, 1 );
my %saw = ( );
my @unique = grep { ! $saw{$_}++ } @arr;

use Data::Dumper;
warn Dumper( \@unique );
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That one line...
my @unique = grep { ! $saw{$_}++ } @arr;
...is where all the action is.

We create a hash (%saw) and the only items that make it into @unique are elements that have not been filtered through grep { $saw{$_}++ }.

Kudos to you though for really thinking through this problem. Just goes to show - There's More Than One Way To Do It!