Chapter 752 of Florida Statutes sets forth the circumstances in which grandparents can file for visitation:
752.01 Action by grandparent for right of visitation; when petition shall be granted.--
(1) The court shall, upon petition filed by a grandparent of a minor child, award reasonable rights of visitation to the grandparent with respect to the child when it is in the best interest of the minor child if:
(a) The marriage of the parents of the child has been dissolved;
(b) A parent of the child has deserted the child; or
(c) The minor child was born out of wedlock and not later determined to be a child born within wedlock as provided in s. 742.091.
(2) In determining the best interest of the minor child, the court shall consider:
(a) The willingness of the grandparent or grandparents to encourage a close relationship between the child and the parent or parents.
(b) The length and quality of the prior relationship between the child and the grandparent or grandparents.
(c) The preference of the child if the child is determined to be of sufficient maturity to express a preference.
(d) The mental and physical health of the child.
(e) The mental and physical health of the grandparent or grandparents.
(f) Such other factors as are necessary in the particular circumstances.
(3) This act does not provide for grandparental visitation rights for children placed for adoption under chapter 63 except as provided in s. 752.07 with respect to adoption by a stepparent.
It looks like you have grounds to file for visitation here because the child's parents are not married.
Florida law also allows for extended relatives of a child to file for temporary custody in certain circumstances. 751.03(8) of Florida Statutes states that parents must either consent to the temporary custody or they must have abandoned, abused, or neglected, the child. Assuming the father will not consent to you having temporary custody, you may still be able to get custody if your daughter consents and you can prove that the child's father has abused, abandoned, or neglected the child.
Please let me know if you have any other questions.
Best of luck!