Google has released an update Version 0.8.1.6252 to Google Search App for iPhone and iPad that has a couple bug fixes but more importantly, it now supports Google Doodles.
Now when you open the Google iPhone app, it will display the Google logo of the day. So if you opened it today, you would see the Charlie Chaplin's live Google logo.
Google Search is a free app and with it you can get the most advanced Google search experience for your iPhone, now with Google Goggles, Voice Search and My Location.
Here's a picture of the Google iPhone Search App with today's Charlie Chaplin's Google logo:
You can download the Google Search app from iTunes App Store.