This obituary for Joanna Lee notes that she was an actress who became a TV writer for shows including Gilligan's Island and The Waltons. And it notes that she became a producer and won awards for TV movies, including "Babe."
But it doesn't mention that she wrote over a dozen episodes of the original prime-time Flintstones series, starting in the show's third season. I'm hesitant to say that makes her the first-ever female writer of animation but at the moment, I can't think of an earlier contender for that title.