You will be filing form I-131 for a reentry permit. The timing is tricky. You absolutely must get your biometrics done before you leave the country, which you can expect to be scheduled within a month and half of USCIS receiving your application. It is possible to leave the country and receive the final decision on your application once you are already abroad.However, if you leave before it is finalized you won't know the result of your request until after you have left the country. It is currently taking USCIS much longer than it has in the past to process an I-131 request. If you want to receive a decision on your filing before leaving, I would give yourself at least 6 months.Keep in mind, the timelines here are approximate. Processing times have been increasing for all types of applications recently and there is always the possibility that there could be some kind of clerical or beaurocratic error in one particular case that delays things beyond the normal timeframe.