Under Florida law, a minor does not, generally, have the ability to choose to choose his or her guardian. However, there may be several options available.
A circuit court has jurisdiction to emancipate a minor age 16 or older residing in this state upon a petition filed by the minor's natural or legal guardian or, if there is none, by a guardian ad litem. The petition would include a statement of the minor's character, habits, education, income, and mental capacity for business, and an explanation of how the needs of the minor with respect to food, shelter, clothing, medical care, and other necessities will be met and a statement of why the minor should be emancipated. If your niece were emancipated, whe would be free to live wherever she wants, including with you. Based on the situation you described, and assuming your niece is at least 16 years of age, this may or may not be a viable option.
If emancipation is not a viable option, you could hire an attorney to petition the court to name you guardian. Under Florida law, you may petition the court for guardianship of a minor if you are at least age 18 and have no felony convictions. The court would consider the best interests of your niece in determining whether to appoint you guardian. Some of the factors that would weigh in the court's decision would include, but not be limited to, (i) your relationship to your niece, (ii) your educational, professional or business experience ,(iii) your capacity to manage the finances involved, (iv) your ability to meet the requirements of the law and the
unique needs of your niece, and (v) the wishes expressed by your niece as to whom shall be appointed guardian. Note that the court may be inclined to appoint separate guardians for the person and for the property of your niece.
Your best course of action would probably be to discuss this matter with a qualified Florida lawyer who is experienced with Florida guardianship law. Many lawyers will provide an initial consultation at no charge.