What is the best time to switch job?

I am thinking to put papers I am currently having 6.5 years of experience and recently I got a offer in a product based company but this is very small US based firm which is having office only in hyderabad in india.

My peers are saying If I put papers now and after notice period I will be released in November and it is a dry season for hiring. Any suggestions which is best month to switch because I want to get offer in MNC since I am having a bad experience with small firms they loaded me with work . I am in a complete dilemma.

Any suggestions will be helpful?