This bio-pic could work but it fundamentally needs a clear and dramatic facing-hefty-challenges scenario. (Which the logline does not portray.) The logline, at the moment, only mildly refers to the author's 'struggles'. This is not enough to inspire a potential producer.
Here's a suggested rewrite: "Ted is a young underemployed dreamer in the fifties. He doodles child-like drawings while barely paying his bills. But Helen encourages him to make a book with his art. Ted's crippling self-doubt, however, threatens the completion of 'The Cat in the Hat'."