How to install Whatsapp on Android 1.6
From the whatsapp site, the minimum requirements are Android 2.1, so even if you managed to find the APK and side-load it onto the G1 running 1.6, it probably will not work.

Stable releases of CyanogenMod 5 (Android 2.1) and 6 (Android 2.2) are both available for the G1.  You can install Whatsapp if you upgrade to CM 5/6.