I wouldn't recommend doing this trip like that.
A. You will be traveling towards the end of season when weather is quite cold and most camps there food around the end of first week of October.
B. You will have just 6 days in hand, including the traveling from Kolkata. This means unless you're flying both ways, you won't really have time to take the route via Shimla and would have to go through Manali. This would result no acclimatisation and direct exposure to high altitude, which increases the chance of AMS exponentially.
With a chid travelling, i can't recommend something of this sort.
Better bet would be to travel in September with 6 days in hand, starting and ending at Delhi. That way you will be able to do Spiti and Chandertal and reduce risk drastically.
Can you please provide me with an itinerary? Starting 14th October 2018 till 21st October 2018If that is the case, then head to Kashmir. You can fly directly to Srinagar and make that your base. Fall season is beautiful in Kashmir, as long as there isn't too much haze. Even if you don't explore a lot of places, you can stay in Srinagar itself and just relax.
Alternatively Tirthan Valley along with Prashar Lake, Sarahan and Kalpa, Dalhousie and Dharamshala in Himachal will make for a good circuit.