No, I don't think the nightingale is brainless. Being simple, innocent, shy or dismissive doest not mean foolish. It is only being noble. She wanted to be a successful and accoladed singer. So, she accepted the frog's advice of giving her vocal training. Her only fault was that she lacked confidence.
Yes I think the nightingle is brainless to some extent because she agrees to receive training from a creature who croaked.
She was not confident of herself .She fell into the trap of laid the scheming frog. She acted on frog's advice which resulted in her untimely death.