My advice would be to distill and add fatal error checking everywhere you call GD functions. I would also separate the $GD->plot( \@data )->png into two calls with error checks on each. This eval example works just fine so it is not the eval that is the issue:

sub graph_vector {
    require GD;
    require GD::Graph::bars;
    my $png = "c:\\temp\\test.png";
    my $GD = GD::Graph::bars->new( 300,300 )
        or die $GD->error;
    my $data = GD::Graph::Data->new( [ [1..26],[1..26] ] ) 
        or die $GD->error;
    my $gd = $GD->plot( $data )
        or die $GD->error;
    open my $img, '>', $png or die "Couldn't open $png: $!";
    binmode $img;
    print $img $gd->png or die "Error printing png: $!:", $GD->error;
    close $img;
    undef $gd;
    die "Got error!\n";
  return 0;
}

eval{ graph_vector() };
print $@ if $@;
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However if you pass null array refs to new() it chokes. I am calling GD::Graph::Data so you can see that error. I suspect you may not be getting the data from your DB.