Discussing death and suicide is not the same as being suicidal. Like kaliope says, I do not think your therapist will be disappointed, upset or frightened. I think the sharing with her can help you with the burden some. You will no longer have to wonder or fear what she might think and feel, you will know. A lot of my mind sometimes gets clogged up with worries about other people but they are not mine to worry about; I cannot know about other people other than what they tell me, the rest if all my imagination based on my own background and experiences. When I discuss things with another person, I can drop all that worry and excess imagining and use that energy to better work with myself.