Thanks for using Ask a Master Gardener with your plant identification.

The sample in the photo has some condition issues which will make my identification uncertain. The sample looks wilted and it would help to have a  photo of the entire plant as well.

My initial response would be French Lavender, Lavandula dentata. The leaves would have a camphor scent differing from the expected lavender fragrance. It would have a lavender colored flower spike when it flowers, which occurs in the fall and winter in areas where the plant can be grown outdoors. Lavender is in the Mint family, which means it would have a square stem. French Lavender would be winter hardy in zones 8-11. We are in zone 6. Zone 8 occurs in the southern half of Georgia and south from there. You should plan on growing the plant in a pot indoors and taking it our for the summer months. Keep it on the dry side as root rot can occur if overwatered. Place in as bright a location as you have.
Here is a fact sheet on this Lavender:

http://mpb.ou.edu/plants/week496.shtml

One thing that is making me wonder on plant ID is the bronzing of the leaves. There are other plants that will have a leaf shape as shown along with the bronze leaf color.
One plant that has these traits is called Brass Button, Leptinella squalid 'Platt's Black'. However, this plant is a very low growing ground cover perennial , only reaching up to 4" tall. Your sample looks taller than that. Here is an information sheet about it:

http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=b785

The last plant with leaves shaped like this would be a succulent house plant called Mother of Thousands, Kalanchoe daigremontiana. Here is information about this plant: 

https://tuckergreenhouse.missouri.edu/mother-of-thousands/

I really do think that you have a French Lavender plant, but these other two fact sheet would help you make a more accurate decision. 
Thanks for your question.