Maybe this is closer to your liking:

#! perl -slw
use strict;
use Time::Local qw[ timelocal ];
use POSIX qw[ strftime ];
use GD::Graph::points;

my @x_vals = (
    '2012-11-07',
    '2012-11-08',
    '2012-11-15',
    '2012-11-19',
    '2012-11-30',
);

my @y_vals = (
    11, 12, 13, 14, 15,
);

# -------------------------------------------
my @epoch_x_vals = map {
    my( $y, $m, $d ) = split /-/, $_;
    timelocal( 0,0,0, $d, $m, $y );
} @x_vals;

my @data = (\@epoch_x_vals, \@y_vals);

sub x_number_formatter { return strftime "%Y-%m-%d", localtime shift; 
+}

my $graph = GD::Graph::points->new(400, 300);

$graph->set(
    x_label           => 'X label',
    x_labels_vertical => 1,
    x_tick_number     => 5,  # experimented with this value a bit
    x_min_value       => $epoch_x_vals[ 0 ] - 1e6,
    x_max_value       => $epoch_x_vals[ 4 ] + 1e6,
    x_number_format   => \&x_number_formatter,
    y_label           => 'Y label',
    title             => 'some title',
) or die $graph->error;

my $gd = $graph->plot(\@data) or die $graph->error;

open(my $img, '> plot.png') or die $!;
binmode $img;
print $img $gd->png;
close $img;
system 'plot.png';
[download]