You are passing $base_index as an additional data set. If you wish to retreive the index you use the index member and pass an optional base. Changling your last few lines to:

my $shannon=Statistics::Shannon->new($data,);
my $output=$shannon->index ($base_index);

print "Index: $output\n";

print Dumper($shannon);
[download]

Prints:

Index: 2.17095059445467
$VAR1 = bless( {
                 'shannon' => {
                                '2' => '1.50478828368119'
                              },
                 'min' => 1,
                 'max' => 3,
                 'data' => {
                             '6' => 2,
                             '4' => 1,
                             '1' => 1,
                             '3' => 3,
                             '2' => 3
                           },
                 'update' => sub { "DUMMY" },
                 'sum' => 10
               }, 'Statistics::Shannon' );
[download]