Frederick encouraged Louisa to be firm and act on her beliefs and I think you are right that she was not mature following his advice. (;D) She was not mature but I also think she was in a fever to please him—a bad combination IMHO. I think his focus on a firm mind is a bit immature in itself because he obviously has not thought of the possible consequences of an always unbending nature. It is no wonder because his unbending nature (from his point of view) has served him well. He was right that he would be lucky in his career and I am sure he is just does not think Louisa would ever be so foolish to do something dangerous or not to take his advice—which is what happens on the Cobb. I think Frederick has his guilt to bear for encouraging Louisa’s obstinacy but she is still responsible for her actions. IMHO JA is so wonderfully precise in teaching Frederick a lesson here. He has disdained Anne for her supposed weakness of character in being persuaded by Lady Russell from the dangers of a possible long engagement and as he sees it also by not believing and trusting in him. Louisa refuses to listen to the dangers and his advice not to jump again from the steps; she is not to be persuaded from her desire as Anne was but her belief in him and trust that he will catch her is as steady as he could ever want. I wonder too if Frederick will make the same connections as Anne about the advantages of firmness of character; (;D) Anne thinks he ought:

Anne wondered whether it ever occurred to him now, to question the justness of his own previous opinion as to the universal felicity and advantage of firmness of character; and whether it might not strike him that, like all other qualities of the mind, it should have its proportions and limits. She thought it could scarcely escape him to feel that a persuadable temper might sometimes be as much in favour of happiness as a very resolute character. (Ch. 12)