To access to my Google Docs, the regular way is go to docs.google.com and search by doc name. To shorten this process, I have a custom search engine in Chrome like http://docs.google.com/#search/%s. So I can search my doc in Chrome address bar. However, this will still go to docs.google.com and list all the results.
Is there any app/extension can search and open the doc right away?
Yes, try the extension "Black Menu for Google"
https://chrome.google.com/webstore/detail/black-menu-for-google/eignhdfgaldabilaaegmdfbajngjmoke
It does what you are asking for: searching your docs and opening the doc directly.
You may want to try out software from www.harmon.ie, which allows you to access GoogleDoc from within MS Outlook.
Install the Google Drive desktop client and use your operating system's built-in search function. Opening the "file" in your local Google Drive folder will open your browser and go directly to the document.
