Greetings Sneha!

Hope you're doing great.

Preparation for CAT generally doesn't requires more than 6 monthns. However, that depend on the student's abiity and understanding. Since you're already sure about giving CAT a try after finishing your graduation, obviously you can do that. I'll suggest focus on your graduation score and try to get as much marks as you can, since graduation marks plays a vital role in your selection process so, having a great Undergrad score will boost your chance of getting selected. 

So, it's upto you if you want to start off with graduation then you can do that else you can just start in the final year of your undergraduation.

Hope this will help. Do reach out in the comment section below if you need any help.

All the best for your preparation!