There's nothing built-in that could do this, but it's doable given a few modifications to set this up, you must have programming knowledge (C#, XML, etc), of course. The best approach I've seen that could do this is to use the EventHandler interface. In the Admin site go to the
EventHandlers menu and find the NewOrder event and set the CallOut URL. You can specify and xmlpackage to use to create an XML document to send (the default event handler package has a small section in it to send data now but it only sends the OrderNumber which comes into the package as Runtime parameter). Since you are needing a lot of order data it would be best for you to create a custom package to generate your xml, the shape of which would be completely up to you.
Alternatively, you could do a bulk export of orders also via the WSI interface. See the
WSI manual for details.