1-2 months is what I recommend as well, definitely not more if you are looking for an entry level job in a social service agency (I do hiring in my current position and I would not hold a case manager position for longer than two months). In terms of getting hired at internships- I was approached by my supervisor and asked but I would recommend expressing interest now to your supervisor. Even if they don't have an opening if they know you are looking they will often point you in the direction of openings in other agencies if they hear of them. Focus on doing really well at your internship, being proactive and going above and beyond.