It depends on you. But it will be better to buy a laptop within 2 months of studying in IIIT Allahabad as everything is digital nowadays and it is easier to learn digitally than the conventional pen and paperwork. Digital learning is a faster method of acquiring knowledge.
Moreover, in the college, every student is allotted a system and that is accessible anytime. You can study, code, or do the rest of the work on the system allowed, like making PowerPoint presentations, taking notes, etc. Even if you don’t have a personal system, you can take help from your friends regarding this.