It is my understanding - and from a little bit of googling around - that there are no breeds banned by law in Germany.
However, there are 4 breeds that are subject to conditions or restrictions (Pitbull Terrier, American Staffordshire Terrier, Staffordshire Bull terrier, Bull terrier). I've heard it depends on the state where you'll be living. You might be required to use a leash (even a muzzle?) unless you can get a certificate from a dog association that your pup is not aggressive.
Since you'll be on base, is there any way to check with the army? They must have already had this question come up before.
Good luck with your move!
mom to 3 lovely kids