You may only be in the first or second month of your final year at university, but it is not too early to begin your graduate job search.
Massive corporations and well-known companies are highly competitive to get into. They have strict and lengthy processes and are only really looking at top caliber candidates: People that not only have the academics and prior work experience but people who are also organised and pro-active - the types of students that don't just apply on a whim and those who have done good research.
Even if the employer is not a massive brand name, to smaller companies with a more interpersonal recruitment process, it can give you the edge and create a good first impression on your potential employer.
Another advantage to starting your job search now is because of time. Your final year passes so quickly - deadline after deadline, exam after exam. It is your final opportunity to make an impact on the grade that you will graduate with. Rather than leaving your job applications to June and July, when the bulk of your exams are and the need to find a graduate job increases, do it earlier in the year so you can get it out of the way and have something secured. You won't have to panic!
Finally, if you do start now, you will have more time to actually explore what is out there. you might think you want to get into a certain industry, but after doing some research or going to a few early interviews, you might realise its not for you. Don't leave it too late!
Overall, beginning your graduate job search early is beneficial and will calm those final year panics!
All the best with your job search!