Yes, your Kerala trip for 6 days can be done under INR 7000, but this will be excluding airfare. For more details on the budget and everything else you would need to plan a trip to Kerala, please be sure to check this link -
Yes Kerala trip can be done under 7k excluding flight tickets, and also compromising on stays and food. Since, Kerala is a rejuvenation hub and to enjoy every bit of it, I would suggest you to take your time and increase your budget a little and then you can enjoy the vibes of Kerala. Under 7k you will miss the essence of Kerala.