No, If the father is involved in the child’s life and has signed the birth certificate. He has a right just as much as the mother does, to even be able to have custody also.
There should be more written her so that you would be able to get a better answer to your question. Is the father in the life of the child spending time with the child him self? Does he work. Was it a planed pregnancy. Does he love his Daughter? As much as you do.
Please take this advice for the well being of your child, that the child will not grow up hating one of the parents. How is your relationship with the child’s father, I went thru this with my wife. You will find that life will be a little easer if you allow the father to be a part of
her life, by going joint custody.
So that you will be able to have breaks in between for I tell you that when he comes to take the child you will feel great to be able to have that break. I know this as a single parent always being stuck at home never getting a break, until she the mother would decide to come and pick up our two children. At this time my daughter was 1 half years old my son 5 years old. I was grateful to be able to have breaks in between.
So you need to think of this and the life situation that you want your child to go through. With love from both parents or feeling that one did not care and for the child to grow up always wanting to find and be with the other parent. something to think about.