Is it okay to start a job right after graduation or is it better to take at least 1 month of rest?

Congratulations on passing your NCLEX. It's personal preference really, but I would take some time off. You just spent a couple of years studying, and you will spend many more years working. You got to have a work life balance. Enjoy what you just accomplished for a few weeks, and then go make that money. Also, make sure you take time off for yourself when you do start working. This job can drain you physically, mentally, and emotionally. So make sure you take time to recharge. You will be a better nurse for it. Hope this helps. Best of luck.

Look for residency programs: they typically start within a few months of graduation to allow time to get licensed. But no, I would not wait to get started. You worked hard to get through school, the payoff is beginning your career.