I'd start with something a lot more limited, such as an overnighter only a couple of miles from your car. That way, if everything goes wrong (it does happen, and is how we learn!), you can easily bail out. You'll enjoy the longer trip a lot more if you're prepared!

Also, practice a lot around home with your gear. For example, set up and take down your tent enough times that you can easily do it. You don't want to be out on the trail on a dark and stormy night trying to set up the tent with instructions in one hand and flashlight in the other!

After some practice under ideal conditions, try an overnight in the back yard or a car campground in nasty weather. Better to learn to cope close to a warm dry bed, or at least your car, than out on the AT!