Hey Eric, there "may" be bears in the area but typically at improved campgrounds like you've selected you'll almost always know if they are heading to your site by listening to other campers banging pots and pans to scare them off from their site. Seems sort of odd but it is a reality, bears are mostly found at popular campsites vs remote camping sites... obviously the bears have learned that groups of humans and camping equals "easy pickings" for food treats.
Shouldn't be a big problem this time of year since the spring brings plenty of food (natural) for bears so it's not like mid-late fall when they are trying to fatten up and are finding native food harder to come by.
Re: ticks, you'll find them mostly if you and the family are hiking in brush and/or tall grass. They "hang out" literally on slightly elevated forest growth (grass and shrubs) waiting for an animal (food source) to pass by and they step off/jump off onto fur, clothing, skin, etc. and find their way to a darker, secluded/protected spot like your waist band, under arms, crotch (nether regions) and the dig in (chew their way into your skin but only shallowly) to feed off your tissue fluid.
If you guys are hiking trails and don't get off trail into scrub, tall grass, bushes, etc you shouldn't have any problem. "Shouldn't" however is the key word here... surprises can happen when you least expect it like a tick or two falling off a limb over your tent and crawling around to find warm meat! If you are sleeping on the ground (rough camping on grass) then the likelihood goes up but it's not too likely at improved campsites. Frequently ppl get ticks and or chiggers (which are another big, itchy, irritating problem) while exploring and gathering firewood. Best bet is to stop at a local convenience store and by a bundle or two of approved firewood - approved it that it is harvested locally, verified as insect free, and safe to use in the National Forests. If you bring firewood from home or from other areas there is a really high likelihood that the wood contains non-native pests (beetles, grubs, caterpillars, etc.) that can escape into the forest and begin another devastating invasion of native trees which are not prepared or are highly vulnerable to insect infestation.
Which provides two reasons to purchase firewood locally - avoid ticks/chiggers and avoid introducing insect predators to the forests you want to see again.
By the way, almost any insect spray or lotion is a good idea to spray on ankles/socks, waistband of clothes, wrists and around your neckline.
One last thing, especially for wife and kids - poison ivy is in full bloom/fury this time of year. Be careful where you walk, put stuff down, etc. the oils are long lasting and easy to spread to all sorts of body sites you'd have never thought of. Like picking up firewood which is either positioned in the ivy or may have ivy as an old dead vine (will still have oil inside). That oil gets on your hands, then you wipe the corner of your eye, or go relieve yourself and find that in the morning your privates are itchy, read, swollen... It is all and experience you really don't want to go through - don't ask how I know this... LOL
Regrets for the long response... but you asked. I'd hate it for you if your wife and 5 YO get into a big discomfort setting while camping and then NEVER want to camp with you again.
Oh, one last thing - no 2 last things, if you wash with soap and water within 30 min - 1 hour after exposure to ivy... you'll typically not have a problem as the oils wash off easily but any tools such as saws, hatchets, shovels, tarps, tents that get contaminated with oil... will have that oil and can easily get on you when you get back home... this includes your shoes/boots. 2nd thing, bring a good set of tweezers with you just in case your encounter ticks. All you need to do is grab their body (assuming they've burrowed into the skin) firmly and then "gently" pull away from the skin... don't jerk or snatch just a slightly firm tug and be patient. They will let go because their mouth parts get tired and then they'll release. If you pull too or jerk fast (too firmly) then their mouth parts or maybe their whole head can break off and be stuck just below the skin. This results in a red, swollen, very irritated "pimple" sort of spot that itches for days. GA "generally" doesn't have lyme disease in the deer ticks you may find - it "COULD" happen but it's not as wide spread nor as prevalent as say Pennsylvania and further north.
In closing, the insects pests, the bears, the poison ivy are all just inconveniences and NOT life threatening. But they are really bad for new campers - for more seasoned folks who've had these maladies befall them - it's just a price of being outdoors and in the forest. "this too shall pass"
Best wishes for your trip and hope this is merely the first time you folks enjoy these National Forests in GA.
