"This is very interesting as a project" What is the next step to obtain PhD position?
The second step is to submit a strong application: Good grades from a good department, a compelling statement of purpose (which reiterates your interest in your target advisor), and strong letters of recommendation that address your research potential in personal, specific, technical, and credible detail. And then write the professor to tell her you've applied and reiterate your interest.

As long as you're building a strong application, you should send it to several other schools as well (minus your interest in that particular advisor, of course).
There is absolutely nothing you can do to guarantee admission to  your first-choice program, so you need to cultivate other options as well.