As per rules, a pet dog can be carried in dog box in Second class Luggage/Brake Van (SLR), or with the passenger in First class and AC First class compartments, provided that the whole coupe (2 berth) or cabin (4 berth) is booked by the passenger or with the concurrence of fellow passengers.
..
Dogs are not allowed to be carried in AC 2-tier, AC 3-tier, AC Chair Car, Sleeper class, and Second class compartments.
.....
more...
In Shatabdi trains -- booking /carrying of dog is not permitted as these trains do not have AC First class and First class compartments and do not have dog boxes.