Domain name change?

Is a 301 redirect enough to tell Google that my site have moved to a new domain?

How much time will it take for the search engine to update its index according to my new domain?

I need to switch the domain in the Google's index ASAP

create an account with Google webmaster tools (its free), add your site to your account, verify you own the site. Then on the left hand side there is a category called "Site Configuration" inside of it there is a change of address link that will assist you in what your trying to accomplish.

Yes....I agree with chano420.

This is the best way to do it...alongside 301