The perfect variant would be within because it sets a time frame. Within a month from now/today. Over means after; over a month has passed and I still haven't received my salary. During is used in the past, during my time at microsoft, i've gained a lot of experience. In is similar to within but it doesn't specify consequences if it didn't happen in a certain time frame / limit. In a month from now we will decrease complaints by 20%. It can also mean that you will start after a month. Within sets a time frame. We need to get the job done within the next hour. It depends on how you formulate the sentence, We need to get the job done in the next 30 minutes. We need to get the job done witin the next 30 minutes. We need to get the job done during those 30 minutes.

with n one month is absolutely correct, its giving you the time limitation you want to achieve, any questions you have feel free to ask (*^▽^*)

Within :-)