I have a 6 week old little girl and her father and I are not married or together. I wanted to know what kind of visitation he would get if we went to court. Right now we are getting along good and he comes over to see her but he keeps bringing up wanting to take her overnight with him and his new girlfriend. I am just not comfortable with this and want to know what my rights are. Also I live in Georgia and I am not breastfeeding. Thank you

Assuming you trust him what are your objections? Separation anxiety is tough on new parents.

You can certainly take him to court and have a visitation schedule setup but there's probably a good chance that he will have overnight visitation at least once or twice a week.
Since you're getting along with him you should try to come to an agreement between the two of you as to a visitation schedule.
Try to remind yourself that it's a good thing that her father wants to be active in her life.

I wouldn't want a newborn to leave for overnight visitation until I knew that he could bathe, change, feed, and put her to bed. What happens if he and the girlfriend have a fight and she walks off; does he chase after her or stay with his daughter? Is his vehicle equipped to transport an infant?

The bigger issue is are you nursing? In most states an infant defined as a child under the age of one will stay with the mother over night all nights if nursing. There are actually some very different laws regarding infants than other children that many don't know about. Just call a local lawyers office and they should be able to tell you over the phone if your state allows over night visitation and such for a child under one year. Other stipulations that go with it are that the father can visit for like two hours at a time at the child's place of residence or other location agreed upon by both parties. But again it depends on your state and also if she is nursed.