Kurt is a contracted form of a the German name Conrad which is shortened to Connie, - a feminine (and masculine) name derived from Constance.
Conrad is derived from the Germanic elements kuoni "brave" and rad "counsel". This was the name of a 10th-century saint and bishop of Konstanz, in southern Germany. It was also borne by several medieval German kings and dukes. In England it was occasionally used during the Middle Ages, but has only been common since the 19th century when it was reintroduced from Germany.
Constance is the medieval form of Constantia. The Normans introduced this name to England (it was the name of a daughter of William the Conqueror).
Related names to Connie / Constance: Cornelia, Cora, Kora, Corrie.
You can also choose a name a girl's name that starts with a "k" and sounds a bit like Kurt such as:
Karen
Kirsten
Katherine
Kara
Katie
Katrina
Kathy
See more suggestions at Magicbabynames.com.