Should I ask for a supervisor change?

I'm a social work and new at my place of employement. I love what do but my supervisor is not someone I foresee getting along well with. She is petty, judgemental, and always looking for what you are doing wrong. Nothing is good enough for her. I do not like this. I want to ask for a supervisor change but it is hard for me because i have been working at this position for only five months. Is it a good idea to ask for someone else to supervise me if I feel uncomfortable around this woman.