Where to begin......I have never lived in Georgia, but have lived in neighbouring states (Tennessee and Alabama). If you are in Atlanta (or a suburb), you are likely to find the adjustment easier as it is a more cosmopolitan city.
Everyone else is correct, there are different words for things and you will probably get some blank stares until you learn to adjust to the local phrases (elevator, trunk, pacifier, drug store, gasoline/gas, etc.) However, people will LOVE your accent and will respond warmly to you based on that alone. It seems exotic and charming to them.
You will drive EVERYWHERE - the cities in the USA (outside NYC, Boston, etc) are spread out and not geared for walking. You will become accustomed to drive through services - endless fast food, banks, dry cleaners and even pharmacies are increasingly common. Can't speak to the differences in car seats though. You will learn to appreciate the "mother and baby" reserved parking spaces which are close to the entrances of many malls/shops.
Georgia will be unbearably hot/humid in the summer, so you will learn to love air conditioning and great piles of ice in your drinks. Be prepared to drink iced tea - it's the drink of choice everywhere! Extra refreshing with a slice of lemon and sprig of mint. You can even have peach iced tea - quite good.
Zebra is correct about circumcision for boys - it's the norm. Don't have any knowledge of reins in public being frowned upon. Really the only time you'll be walking in traffic should be to/from the car unless you live on a busy street.
Many of the mums I know/knew did breastfeed. It is not unusual. However, it was my experience that the women are much more modest about feeding in public and would usually prefer to pump and feed from a bottle when away from home. Many are anxious/paranoid about a glimpse of breast in public. If I was out, I often found it most relaxed/comfortable to simply go back to the car and breastfeed. However, I did nurse once on a bench at a street fair. If anyone noticed, they didn't say anything.
In my experience, many of the stay at home mums don't really do toddler groups. You meet other mums through organised activities (baby music class, gymboree which is the US version of Tumbletots, etc.)
You will be amazed to see the number of churches in the south, and the huge size of their buildings. Many churches have nursery/kindergarten programs as a way of utilising their buildings during the week. The churches with nursery/kindergarten programs also usually offer a "mother's day out" program one or two days a week for mums of babies/young toddlers. It was my experience that mums dropped their kids and ran out the door to food shop, exercise class, etc as this time was precious time to themselves - in other words, there was little lingering and chatting with new faces.
You will be amazed to see the size of the living space people have there - huge. My two bedroom flat here is literally HAlF the size of my two bedroom flat in the USA. You'll be interested to know that estate agents there are not allowed to advertise a room as a bedroom unless it has a closet. You'll be pleased/shocked at the generous size of the secondary bedrooms.
Many people still smack, but there are many who don't. There are plenty of enlightened people who look for more constructive ways to discipline, and there are others who think there's nothing wrong with a smack. I will say though that most people I know were smacked as children, but don't smack their own kids. So, perhaps it's a generational, cultural and socio-economic thing.
I think the most important thing is to realise that it will take time to find your feet. Don't be depressed when I say that after about 2 years you should have it sussed, and should have the beginnings of some real friendships. But, isn't that about the same for most any new place? Personally (and it's a sweeping generalisation), I would gravitate toward areas where academic professionals live and send their children to school. They tend to be highly educated, comfortable but not obnoxiously wealthy/showy, not overly religious, aware of the world outside the USA, more tolerant/curious of differences, etc.
I could go on and on. But, I'll stop now. Feel free to ask me anything else you think of, and I may add more as it comes to mind.