PhD problem: a new student has the same idea as me
You should probably talk to your advisor and possibly arrange a meeting with the other student, her advisor, your advisor and yourself. You need to sit together and discuss how your work and her work are going to differ, because nobody has anything to gain from two competing PhD students undermining each other within the same research group. Once you have fixed boundaries, you will be free to go your own way and collaborate on the common parts, which will benefit both of you.