If I started studying for a CFA Level 1, within the next month, will I be able to p the December exam this?

Frankly speaking, the CFA website recommended studying 250 hours, but nonetheless it does not mean that you could fully understand and p the exam by studying 250 hours. As what you had calculated earlier, you might be able to finish study within 4 months. However, life is always unpredictable; you might get distracted at a bad time and thus influence your study progress. Therefore, I will suggest you start study right now. Besides studying the textbooks, you can also spend some time to do research, try to gain extra knowledge which helps in your CFA exam. Of course, you can still spend the rest of time to do revision before sitting for the CFA exam. Always bear in mind, the more time you spend on studying will helps you understand better.