If Google Trends gives a correct approximation, people stopped searching in Google drastically after approximately one or two months. Six months after the quake the attention to Haiti in Google went back to pre-quake levels. Similar results are for the earthquakes in Japan and Chile.
Google Search Data is a powerful tool for innovative research. Two resent papers for example use it: one to determine if attention in Google for certain stocks predicts stock prices, and the other one (HT: Social Science and Statistics Blog) to study the link between "racially charged" searches and voting for President Obama. This approach (the use of Google Search Data) has also been used to predict outbreaks of Influenza (see the paper here). This is just fascinating !!! . . . and the application are numberless [imagine what it can do for your research].