I am from Dubai and would live to visit Darjeeling, gangtok and Bagdogra in 7 days....Can I do it ? I will fly?

I am planing a holiday to Darjeeling. I will be flying from Dubai to Calcutta and then take a flight from Calcutta to Bagdogra and then travel by car to Darjeeling, Gangtok and Siligiri. I want to do this in 7 days and return back...... Is it possible ??