Tread carefully. You don't want to submit a resignation letter unless you are positive that you have a job waiting for you.
- Make sure the new employer is okay with waiting 2 months
- Make sure you have the new offer in writing
- If not, check with an employment lawyer before submitting your resignation letter
Will the new job wait 2 months?
The worst case scenario is that you submit your resignation, serve your notice period, and discover that your new employer couldn't wait that long and no longer has a position for you. You say:
The reason why I want to put it at 1 a month is new employer needs me as early as possible. I set expectations that it would mostly take 2 months, but though this is my attempt.
This suggests that you may not have had this discussion with the new company, and they may not know when you can join. This could be a serious issue, so you should confirm with the new company that they are willing to let you start working in two months rather than after just one.
Get it in Writing
Even if they tell you, "No problem!", make sure you get a signed employment contract that clearly states the offer is available for you starting in two months. You don't want to get just a verbal commitment, and then find out after you've resigned that they couldn't wait and ended up hiring someone else instead.
(You may want to check the new employment contract to see what the notice period is for the new job as well, just in case you run in to the same situation when you move on to your next job).
Check with an Employment Lawyer
In some jurisdictions even with a contract stating your notice period is 2 months, there are laws that limit that further. If your new company is unwilling to offer you the job if you have to serve that notice period, it may be worthwhile to discuss with an attorney to make sure you understand what the law says about your current employment contract.
Here is an example from Japanese law:
If an employee on a labor contract with no set term of agreement wishes to resign (i.e., the employee wishes to terminate the labor contract by notifying the employer of his/her intention to do so), the employee can do so by providing two weeks' notice. Furthermore, although there is no firm legal precedent, the prevalent doctrine is that even if a company work rules stipulates that employees must give more than two weeks' notice, it is without effect in cases where the rule sets an unreasonable period.