Recently WhatsApp added the ability to send documents via their beta app, but users were not able to attach documents directly, only being able to send documents via the built-in OS sharing feature.
Whatsapp has just pushed out a new updated to their closed beta application, taking it to version 2.12.310.
The update adds a new Document Attach button to the app, making it even easier to send documents. The feature will only work if both users are on the latest version of the app, which is unlikely until the feature becomes available to the mainstream version of the Windows Phone app, or of course if you are sharing to Android users.
For now you can download the public version of the app from the Windows Store.