guardianship

[hamptonhurricane]

I am a grandmother of a 2yr. old girl. My son (her father) is currently in jail. My son and her mother were never married and as of right now my son has no legal right to her because he was not put on birth certificate but the mother is collecting money from the state and has stated that my son is her father. My question is the mother wants to go to flordia and live with her boyfriend and go to school. She wants to leave the little girl with me until she gets out of school. Can the mother and I write up a paper to give me guardianship of the little girl while she is in school and have it notarized or do we have to go through an attorney and have it done. Also is there a law in Tennessee that can prevent her from moving the girl to Flordia because once that is done we will never be able to see her again.
Any help would be greatly appreciated.