A grep might be a bit simpler. I'm not sure why you push the first element outside of the loop and then have to test for element number inside. It seems to be an un-necessary complication.

use strict;
use warnings;

my @pets = qw{
   gerbil
   parrot
   hamster
   cat
   poodle
   goldfish
   };

my @doubles = grep m{(.)\1}, @pets;
print qq{$_\n} for @doubles;
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The output

parrot
poodle
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I hope this is of interest.

Cheers,

JohnGG