'kyrios' is used 720 times in the New Testament. It can be translated 'Lord," "master," "sir," "owner," etc. It is NEVER translated "God." It is a respectful title which may be applied to God, and often is, but not necessarily.
The word for God, "theos", was NOT used by Elizabeth.
Yes, Jesus is God, but Elizabeth did not address Mary in terms of her son being "theos," but rather "kyrios."
The fact that Jesus was God Himself was a very difficult thing for people to accept, despite the fact that Jesus identified Himself as God during His ministry on earth.
Mary was the mother of the body God used on earth. She was NOT the 'Mother of God'. That is a title that came down from paganism regarding Semiramis, the wife of Nimrod. The Mary of the Rosary, again, is NOT the Mary of the Bible!