NC does not recognize “legal” separation. You are considered separated the day that you begin living separate and apart from each other. After one year one day of living separate and apart either party may file for absolute divorce.
Getting a separation agreement would go back to the date of separation and is not a necessity to be separated. The agreement would make separation and divorce smoother to transition because it divides marital assets and addresses things such as visition, child support, custody. A separation agreement could also protect either of you if a 3rd party gets involved in that it could spell out that while separated you would live as though you weren’t married. This is in some agreements so that it shows it’s agreed that either spouse is alright with the other dating.
If you move out for three months, you would be separated. If you moved back in, you would be reconciled.
I suggest that if you plan to move out for three months, and your spouse is in agreement that this may help a separation agreement could wait. If the 3 months shows no progress and you intend to make it permanent then you will need to consult an attorney. In fact, it may be a good idea to consult an attorney regardless. Though you do intend to take care of your responsibilities, you would not want your spouse bringing abandonment issues into this. Make sure that the intentions are spelled out, recorded and known by each of you prior to doing anything.