There's no statistical evidence that dentists have a higher suicide rate than any other profession. In fact, there's not much data available that correlates profession to suicide rate and very little evidence that profession plays a significant factor in someone deciding to take their own life.
However, in the US the second leading cause of death in the U.S. among those age 15 to 24 is suicide so from that we may be able to deduce that the "profession" with the highest suicide rate is "student"!