My therapist has 9 years of experience, I thought she had more since she's 53 but this is her second career.
Nine years experience is fine for me, I would not want a newbie but the most important thing is for her to be older and a woman. I would find someone younger or closer to my age humiliating to talk to, I would compare myself too much to them, it would not be good or useful for me.
I also find "older" comforting, especially older women (although of course not all of them are!).