I agree with you both Ramya and Louise. I think Fanny she's a serious girl, not likely to joke herself, but can find humor elsewhere.

Those are good instances of Fanny's amusement, but notice that in neither instance is the humor at her dearest objects'(Edmund & William) expense. While they were fighting over the play she was amused, but Edmund hadn't joined in yet. Once he did it was all misery now. ch16

I agree Louise that she does take those instances too seriously and should lighten up. I don't think she's a killjoy necessarily because she doesn't actually confront Mary when she makes the jokes. I think she's not meant to be perfect, and Austen likes to make fun of her too. That's a bit of what I think is why she takes these things so seriously. I'm finding more instances than ever before where Austen pokes fun at Fanny. I like Tom P2's comparison to Winnie the Pooh (one I hadn't considered before.)