I can tell you how Becky behaved, but you're going to have to decide whether her behavior was realistic or stereotypical, and only you can explain why you think so. This is a subjective question, which means that the teacher wants your opinion. No matter what your answer is, it will be appropriate (unless you refuse to answer it or answer sarcastically) because it will be your opinion.
In my opinion, Becky reacts the way most people would, whether male or female. At first, she panics, and then she seems to lose faith and accept that they're lost and might never get out of the cave.
She sank to the ground and burst into such a frenzy of crying that Tom was appalled with the idea that she might die, or lose her reason. He sat down by her and put his arms around her; she buried her face in his bosom, she clung to him, she poured out her terrors, her unavailing regrets, and the far echoes turned them all to jeering laughter. Tom begged her to pluck up hope again, and she said she could not. He fell to blaming and abusing himself for getting her into this miserable situation; this had a better effect. She said she would try to hope again, she would get up and follow wherever he might lead if only he would not talk like that any more.
Tom remains calm, in my opinion, so that Becky won't totally give up. He keeps telling her that the others will find them and they'll be rescued. In my opinion, if Becky weren't with him, Tom might panic too!