Under normal circumstances, neither she nor you can keep the father & child apart. That does not mean, however, that he automatically get what he wants. Most courts are extremely reluctant about removing an infant from its mother for a week at a time; it certainly won't happen if she is breast-feeding. Standard visitation (every other weekend, extended summers, etc.) typically doesn't start until a child is at least a year old. Until then, the father would typically have numerous shorter visits over the course of the week.
I will tell you, however, that, at least in my part of the State, alternating weeks with each parent is not uncommon (yes, I know that's a double negative) once the child is a little older. That depends, of course, upon parents' work schedules, distance from each other, etc.
All that being said, the father also has obligations, most especially the obligation to support the child. Be aware, however, visitation does not depend upon payment of child support or vice versa.
Your daughter needs to file a Petition in the child's home county to establish custody, visitation, child support, etc. Don't wait until he files.
----The advice given here is not intended to, and does not, establish an attorney-client relationship. Also, the advice given is general, based solely on the facts stated in the question. Other facts, not listed here, as well as the contents of any documentation involved in your case may substantially affect your rights/obligations. The only way to know for sure is to schedule and appointment with an attorney to discuss your case in detail.----