Are psychologists more immune to psychological problems? Does knowledge of a psychological problem prevent (or enable one to better defend) the development of psychological issues? For example, if a person has studied about depression and is familiar with the causes and cures of it, is that person more able to prevent himself/herself from going into depression?

Are there statistics about the ratio of mental health problems among psychologists and therapists vs the general public?
Barriers to Psychologists Seeking Mental Health Care by Jennifer L. Bearse, Mark R. McMinn, Winston Seegobin, and Kurt Free of George Fox University asks a similar question.


  Professional psychologists provide help to people in need, but how freely do psychologists seek psychotherapy themselves when facing personal challenges and struggles? What obstacles make it difficult for professional psychologists to seek psychotherapy? A survey of 260 professional psychologists (52% response rate) was conducted to investigate the frequency of various stressors impacting professional psychologists and the barriers they experience in seeking mental health services. Though none of the stressors were rated with particularly high frequencies, burnout was identified as the most frequent problem. Difficulty finding a psychotherapist and a lack of time were identified as the greatest obstacles to seeking psychotherapy. Practice and training implications are discussed as well as future research directions.


As I have said in a previous answer - see for more info., there is Clinical Supervision, which is standard practice and required in codes of practice for registered counsellors, psychotherapists, psychologists, psychiatrists, etc. and those in training. However, what is concerning is that I came across an article by Els van Ooijen in Therapy Today, November 2015, Pg 32 that said


  The number of supervision training courses is ever increasing, yet it is not uncommon for practitioners to receive supervision from untrained supervisors. During my 15 years’ experience as a supervision trainer I have heard many stories about the kind of supervision people receive, ranging from excellent and supportive to unhelpful and traumatic, with many shades in
  between.


An article in Quora listed the following research but the references information provided is not all that great so where I could I found the referenced articles and linked them below.


  One study found the lifetime rate of depression in psychologists and social workers to be higher than that of the general population. (Deutsch, 1985)
  
  Research has shown that female therapists commit suicide at higher rates than the general population. (Roeske, 1986; Steppacher &amp; Mausner, 1973)
  
  In one study, 61% of their sample of psychologists had experienced at least one episode of clinical depression. Of the 84% who had received therapy treatment, 29% had reported suicidal feelings and 4% had made at least one suicide attempt. (Pope &amp; Tabachnick, 1994)


Non Linked References Above

Roeske, N. (1986), Risk factors: Predictable hazards in a health care career. In C. Scott &amp; J. Hawk (Eds.), Heal Thyself: The Health of Health Care Professionals