Andy,
As soon as the days start to really warm up, get your tree outside, and gradually introduce it to a full sun location. I'd repot that treelet in a 5 gallon container and sink it halfway into some surrounding soil. Let those roots wander, and get some good strong growth on that tree. Inside your house is no place for a fig tree. It will just get weak, and not put out many figs, if any. leave it outside in a pot that small and it will dry out and cook those roots in a few hours. You need some more soil volume, and moisture, around those roots. Some Granular Limestone too.
The developing fig is probably a breba. If it were my tree, I'd pull it, and wait for stronger growth, and then main-crop figs....but not too many. Your tree is very small. With good culture, your tree should triple in size, at least, by the end of the season. Figs will come when the tree gains strength and enough leaves to support the fruit. Build strong, stem(s) and branches, first....the rewards will come later.
Good luck, and happy growing season.
Frank