I'm going to tell someone who I've only known for about 2 weeks about my suicidal thoughts and make myself her problem.
Why do you want to tell this person about your suicidal thoughts?
She seems strong enough to cope with it.
I understand wanting to tell someone about your suicidal thoughts, but you shouldn't dump your problems on this person that you've only known for two weeks. If you want help with this problem then you should talk to a therapist or other professional, as they're trained to deal with it.
I'm telling this person everything!
This person is not responsible for your problems especially when it comes to suicide. This is too much to ask of someone who is not a mental health professional. Don't dump your life on her.