The EEEbuntu works just fine on the EEE 1002HA. Just make sure that you select EEE 1000H from EEEbuntu config and you will be all set to enjoy EEEbuntu on your EEE PC. Everything works (incl WiFi) just the same way it works on the EEE 1000H. Here is the screenshot of EEEbuntu running via live DVD.
read EEE 1002HA review