This seems a bit tricky, Selda, and you're right to be cautious. I don't know the prose poem by Kincaid, but I can only imagine that the whole approach is fundamentally different, in technical/literary terms, to 'The Bell Jar'. This could possibly be useful ... but only if the style/approach of each had some direct relevance to the research question. I presume that the research question must have something to do with the themes & message of each work - since what else would two such radically different genres have in common? Does each work have something distinctive to say about the protagonist? Or about human nature? Or what?
I think the IB would accept in principle the comparing/contrasting of two different genres ... but only if, in practice, there is some credible argument for doing so. I would require the student to (1) explain clearly what point she is trying to make, and then (2) produce a very clear and explicit research question addressing the point.
The extended essay is an IB core requirement, where students explore a subject in depth. The subject must relate to one of the courses offered in Groups 1 - 6 of the IB Diploma Programme. The extended essay is an opportunity to demonstrate research and writing skills, along with other traits of the IB learner profile. While independent study and self-discipline are part of this task, an in-school supervisor is assigned to each student to monitor progress. The final, formal piece of writing of 3,000-4,000 words is something that students can be proud of, present to teachers, parents and even future employers.
The following pages explain the relevance of extended essay to Group 1 and the Language A: Language and Literature course. You can find information on the basic requirements and the assessment criteria, along with sample extended essays from former students. It is recommended that you study these pages carefully before you engage in the writing process, in order to ensure the best results and the most rewarding experience.