You should tell your T about it, she can help you with it (hopefully). Your T can't call your parents without your permission, at least not in my country, I don't know the rules in Canada. You haven't had those thoughts in a while, so it would be a bit extreem to send you to a hospital. If you would really have plans then she can do that.
I've had those thoughts a lot in the last year. Every day, multiple times. Until I found meds that worked. Now those thoughts are much less. My T and Pdoc knew about it. I didn't talked much to my T about it, I think maybe one session. She also hasn't asked me about it. Pdoc asked about it at almost every appointment. Both have never suggested that I should go in-patient or something like that. My T told me what I should do if I planning to take action (call her if it's during her workhours and call the doctor). But that's it. Though I kept some details to myself.

But T's can be very different. Some will want you to go to the hospital, while others are just fine with keeping the therapy as it is.
When I was 18, I was in intensive group therapie (you live there 5 days a week and in the weekend you're home). I once took an overdose. it wasn't an attempt, but a sort of cry for help (long story). They send me home the day after, a time-out of a few days. And they didn't offer any help for during that time-out, no advice, nothing about what I should do if I would be in a crisis or something. So it wasn't an attempt, the man who decided about this called it an attempt.

So you never really know what a T would do when you mention suicidal thoughts.