<?php

$collection = Mage::getModel('sales/order')->getCollection();
$collection->addFieldToFilter(
     'updated_at',
     array('from' => $dateStart, 'to' => $dateEnd)
);
$collection->addFieldToFilter(
        'status',
        'complete'
);

foreach ($collection as $order) {
    $items = $order->getAllItems();
    foreach ($items as $itemId => $item) {
        $cats = $item->getCategoryIds();
    }
}

?>