Welcome to BYC!
As others have said, selling shell eggs (that is, eggs for human consumption) varies by
State law. Even whether or not they are called "shell eggs" varies by State. Likewise, how you can display and sell them - what information you must provide, what words you can't use, even how they are packaged. GA even has
candling requirements, unlike many States.
You can also look into selling hatching eggs. Generally, that's unlicensed. Inside the State, it requires very little other than eggs that, more likely than not, are fertile. Craigslist is a popular marketplace for them. If you are close to a State line, you want to consider NPIP certification - its voluntary, but its also the only cost effective way for hatching eggs (or hatched birds) to cross State lines. Of course, the
GA poultry lock down order may complicate things considerably.
Now, a bit of a caution. The egg business is VERY narrow margin, in the best of times. Plenty of people jump in both feet, imagining a cottage business that more than pays for their hobby. The reality is that these are the most expensive eggs you will likely ever eat. Made worse currently, becuase materials prices for coops are way up, and feed costs are (relatively) astronomical.
I've been doing what you are considering, though down in FL. A few months out of the year, I break even or post a small profit against feed costs. Most of the year, its a loss - and that's before considering the expenses of doing it behind a business, with annual coproprate reports to file and the better part of ten hours doing my business' taxes (first time, will be much fast next year, likely 3 hours or so). My personal taxes take about 40 minutes.
Recommend taking a good hard look at your entertainment budget, and decide how much of it you wish to invest/sacrifice in your egg-producing dreams.