My first tought would go to creating my own extension with an observer for the checkout_submit_all_after
event.
This event covers both front- and backend orders.
You can get your order object(s) like this in your observer:
if ($observer->getEvent()->hasOrders()) {
$orders = $observer->getEvent()->getOrders();
} else {
$orders[] = $observer->getEvent()->getOrder();
}
foreach ($orders as $order) {
//call here
}
}
I have also done a couple of ERP implementations where the client wanted a daily cron to sync the orders, the choise is up to you. In this case you will also create a custom extension that handles this.