Do you have a transcription of the record you posted? I believe it is the marriage record for Karen and Laust. I believe it says they are both working in that village that starts with a B. I think it says Karen is born in Andkjær, a village in Gauerslund sogn/parish in Holmans herred in Vejle amt. Birth etc records are registered in the churchbook (not a county courthouse), so it is the name of the parish that is given as the place name for a birth. So yes she is born in Gauerslund sogn.

In addition, to my eyes it looks as if the record refers to Karen's father as afdød Hans Christian Hansen, banevogter. The latter is a job title. "Afdøde" means deceased - the late Hans Christian Hansen.

All best