Is there a way to let my daughter's father have custody without having to go through Mediation to write up an agreement?

Yes, but parenting plans are complex. It really should be completed with both parties sitting down with an attorney. Now that attorney could be a consulting attorney, one who meets you at the law library because he might not have an office. Expect he would charge around $65 an hour to help both of you fill out the forms. Was paternity established or his name placed on the birth certificate? Is the child now over 2 years of age if on the birth certificate?

There are some procedures that need to be followed in order to change custody.