1) If you are rooted-> Go to data/app and there you can find whatsapp apk file. Just transfer it normally using bluetooth or whatever.
2) If you are unrooted-> Create a new folder
Apps inside your internal sdcard .Download terminal emulator. Open it and enter the command
cp /data/app/*.apk /sdcard/Apps. This will transfer all the installed packages in APK form including whatsapp apk. It may take sometime depending on number of apps you have installed. You could also just minimize terminal and wait.
3) As others suggested, you can also download from third party site on web.
A note though, as far as I can remember, whatsapp will persuade you to install new versions and wont let you use older versions. But again, I could be wrong so feel free to give it a try.
Hope this helps :)