Magento 1.9 Category – Get Category Tree as an Assoc Array

In my magento, I have the following category tree structure like this (note: only a few categories has been expanded):

I would like to generate an array that looks like this:

$categories = [
    'Default Category' => [
        'HAIR' => [
            'Hair Colouring' => [
                'Permanent Hair Colour',
                // ...etc
            ],
            'Styling' => [
                'Gel / Wax / Paste / Po',
                // ...etc
            ]
        ],
        // ... etc
    ]
];

Is this possible? It would be a bonus if I can get the product count in each category node; just like in magento admin backend; for example: Hair colouring (1840)

I have been searching online and I found this code (my starting point):

http://magentotutorial.in/how-to-create-categories-tree-structure-in-magento-programmatically/

But it doesn't quite work, this is what I get back: <ul></ul>

Update

After doing some further searching, I had some luck loading the category tree data (linearly) like this:

<?php

require_once 'app/Mage.php';
$app = Mage::app()->setCurrentStore(Mage_Core_Model_App::ADMIN_STORE_ID);

$categoriesArray = Mage::getModel('catalog/category')
        ->getCollection()
        ->addAttributeToSelect('name')
        ->addAttributeToSort('path', 'asc')
        ->load()
        ->toArray();
$categories = array();
foreach ($categoriesArray as $categoryId => $category) {
    if (isset($category['name']) && isset($category['level'])) {
        $categories[] = array(
            'level'  => $category['level'],
            'label' => $category['name']
        );
    }
}

print_r($categories);

This produces the following output:

Array
(
    [0] => Array
        (
            [level] => 0
            [label] => Root Catalog
        )
    [1] => Array
        (
            [level] => 1
            [label] => Default Category
        )
    [2] => Array
        (
            [level] => 2
            [label] => HAIR
        )
    [3] => Array
        (
            [level] => 3
            [label] => Hair Colouring
        )
    [4] => Array
        (
            [level] => 4
            [label] => Permanent Hair Colour
        )
// etc...

I am just now trying to figure out how to parse this output in the structure I want (as shown above).