There is no reason why a woman should not visit a female doctor for the purpose of examination and diagnosis, so long as she adheres to the guidelines prescribed in Islam with regard to uncovering the ‘awrah. These guidelines are discussed in the answer to question no. 5693.
With regard to internal exams by hand or using a speculum, this does not break the fast. In the answer to question no. 38023 there is a detailed discussion of the things that break the fast and things that do not. It says there:
Among the things that do not break the fast are:
Insertion of anything into the vagina such as pessaries, or a speculum, or the doctor’s fingers for the purpose of medical examination.
Insertion of medical instruments or IUD into the womb.
Anything that enters the urinary tract of a male or female, such as a catheter tube, or medical scopes, or opaque dyes inserted for the purpose of x-rays, or medicine, or a solution to wash the bladder.
And Allaah knows best.