Use an Array of Arrays (AoA), definitely. But, flip your thinking. I'm going to assume that you mapped your problem directly to your data structure and set up your outside array as the rows and your inside array as the columns. Flip it.

Set up the outside array as your columns and the inside array as your rows. Now, creating a new column is simple and adding an entry to an existing column is still easy. Maybe something along the lines of:

sub new
{
    my $class = shift;
    my ($max_rows) = @_;

    my $self = bless {
        max_rows => $max_rows,
        data => [],
    }, $class;
}

sub add_column
{
    my $self = shift;
    push @{$self->{data}}, [];
}

sub add_value
{
    my $self = shift;
    my ($x, $y, $value) = @_;

    return unless $x <= $max_rows;
    return unless $x >= 0;

    $self->{data}[$y][$x] = $value;
}

sub get_value
{
    my $self = shift;
    my ($x, $y) = @_;

    return $self->{data}[$y][$x];
}
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