You book 2 or 4 names in a single ticket - Go to CCM/ACM/DCM and submit application for coupe/cabin allotment by citing reasons - Come back to the station and book your dog - Pay Charges.
On the day of boarding check whether you have been allotted coupe/cabin. If not, talk to TTE and request for the same again citing the reason of carrying a dog. Do show the request letter submitted for allotment of coupe/cabin and payment details for booking the dog.