any hint on how may I make it more "perlish"?

Maybe not more Perlish, but certainly a little easier to read:

my $poem = 
   # Line #1
     $words[0][rand @{$words[0]}] . " are "
   . $words[1][rand @{$words[1]}] . " "
   . $words[2][rand @{$words[2]}] . "?\n"

   # Line #2, etc...
;
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Update: This reminds me of the silly-senetence-generator I hacked together for my young son a few years ago:

# Random silly sentence generator.

use warnings;
use strict;

my @nouns = qw(elephant dog man carrot ocean);
my @verbs = qw(is seems appears wants_to_be);
my @adjs  = qw(hairy smelly purple grimy wobbly);
while (1) {
    my $noun = $nouns [ rand @nouns ];
    my $verb = $verbs [ rand @verbs ]; $verb =~ s/_/ /g;
    my $adj  = $adjs  [ rand @adjs  ];
    print "The $noun $verb $adj.\n...";
    <STDIN>;    # Hit "Enter" on your keyboard for a new sentence.
}
# Ctrl-C to exit.
[download]