Before you get started you need to do a few things:
1) You need a file manager that lets you manage and backup applications you have installed on your phone. I use Astro. Install that onto both devices.
2) I transferred the APK between devices using standard bluetooth, if you want to do that then you need to activate bluetooth on both devices and pair them.
3) Almost forgot, make sure you have 'Unknown Sources' activated in the 'Applications' settings options.
So what you do is:
Enable bluetooth on both devices and make sure they are paired;
Use the Astro to make a backup of the whatsapp application. In Astro this is done via the 'Tools' menu item and the 'Application Manager/Backup' option. Select the app(s) you want to back up, then hit the 'backup' button. Backups are stored on the sdcard in the 'backups/apps' directory and should be called com.whatsapp.apk or similar. Navigate to that directory;
Long-press on the apk to activate the pop-up menu, select 'Send', then 'Bluetooth' (if bluetooth isn't available as an option then check that you have activated bluetooth). Select the flyer from the bluetooth devices list. The file transfer will start.
Now you have to switch to the flyer and accept the incoming file via the notifications panel.
After it's been transferred you just need to activate it from where it is listed in the the notifications dropdown and elect to install it. It wont install if 'Unknown Sources' is not enabled.
From there you should be able to register whatsapp. Note that each of your devices will show up as different users to your contacts on whatsapp.
Hope that helps.