My question involves child support in the State of: FL

I am married and I had a child outside my marriage in 2004. I have been paying $500 to the mother of my child since birth, a verbal agreement we made to ensure it would assist with day care. She has been in school now for 2 year so no longer requires day care but perhaps after school care. I am retired military, therefore, I took the initiative to place my child on my DEERS program so that I could provide the medical care and other benefits for my child. I also supply my child with whatever she needs outside the child support money. The mother of my child earns more than I do so my question is, was the $500 agreement reasonable or too high? I provide everything that a custodial parent would do for their child, the only difference is she lives with her mother. I am considering on having the child support office place me on child support just so it can be official. My name is on my child's birth certificate but she does not carry my last name. If placed on child support, can my daughter then carry my last name? I am also wondering if joint custody would be an option without the child support since she makes more than I do, I provide my child with military benefits, and I provide for her as her mother does if not more. There are no child support orders on me at this time.