NLC and PTN are some of the big transport companies transporting ur own car isnt a bad idea but chances of damaging ur car are present while loading and unloading, atleast a minor scratch
One way would cost you around 10,000 that makes a 2 way of 20,000
its better to rent a car from a reputed firm such as metro cabs or euro-cars it shouldnt cost you more then Rs.1500-2000 a day for a corolla i guess.