Your employment contract should be terminated with effect from the end of the month.
Your notice period is one month. The notice period for your employer is two months and is not related to the length of your employment (Section 7:672 (6) Dutch Civil Code).
Your employer may agree a longer notice period for you in your employment contract. In this case, the same notice period applies for your employer as for you, the above as provided for in Section 7:672 (8) Dutch Civil Code.