Hi sophiewilliams,
Searching for a birth of a child named Kathleen in 1914 (with no surname entered in the search) and mother's maiden name Goode, only produces one result.....
Kathleen Clarke, Sept qtr, Huddersfield, vol 9a, page 541.
If she wasn't registered with the name Kathleen, or not registered at all, then this is not a relevant result but it just may be her.
P.S. added information. Sorry may be a red herring as there is a possible sibling for this child 3 years later. However, confusingly there is another Clarke/Goode baby in the same quarter as the one I mentioned. Obviously she can't be a sibling and it's on a different page, so not a twin.