Do dogs go through menopause if so When?

No, menopause is a primate-only event in which menstrual cycles become erratic and then cease. As dogs do not have menstrual cycles, they do not go through menopause.

Dogs have estrus cycles, and under certain conditions can go through a period of anestrus when they stop having estrus cycles. Late in life, a female dog may permanently go into anestrus, but this is not all that common.