Sure. Until and unless you file a divorce, she's free to do as she pleases. Note that filing a divorce before she moves will likely prevent the move until and unless a judge okays it, so you should be in a lawyer's office Monday. Some counties have a standing order that bans the move, and in others you could seek an order.
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Yes, she can move - presuming that you are both the children's legal parents (and you've said nothing in your post to indicate otherwise). Since you are married, until such time as a court orders otherwise, you both have equal rights to the children. It looks like you and your wife are living in Tattnall County? You should find out if the Superior Court has an Automatic Domestic Standing Order the proscribes a party to divorce from leaving the jurisdiction with the children. Speak to a family lawyer in your area.
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I agree with my colleagues. I suggest you speak with an attorney and consider filing for divorce. If you do not do anything and allow her to move, she will likely obtain jurisdiction in another state which would not be good for you in the event you decided to pursue a divorce. At this time, she can move since you have not filed for divorce. Good luck!