Fanny's at her first dance, but no special measures are taken for her. She dances four dances, but we don't know exactly with whom, and then she's listening to Mrs. Norris's and Mrs. Rushworth's myopic gossip, when Tom Bertram comes in and is talking about a horse and picks up a newspaper, she thinks it would be too much to hope he would ask her to dance. The following I find strange and then funny:

"When he had told of his horse, he took a newspaper from the table, and looking over it, said in a languid way, “If you want to dance, Fanny, I will stand up with you.” With more than equal civility the offer was declined; she did not wish to dance. “I am glad of it,” said he, in a much brisker tone, and throwing down the newspaper again, “for I am tired to death. I only wonder how the good people can keep it up so long. They had need be all in love, to find any amusement in such folly; and so they are, I fancy. If you look at them you may see they are so many couple of lovers—all but Yates and Mrs. Grant—and, between ourselves, she, poor woman, must want a lover as much as any one of them. A desperate dull life hers must be with the doctor,” making a sly face as he spoke towards the chair of the latter, who proving, however, to be close at his elbow, made so instantaneous a change of expression and subject necessary, as Fanny, in spite of everything, could hardly help laughing at. “A strange business this in America, Dr. Grant! What is your opinion? I always come to you to know what I am to think of public matters.”

After that he does dance with Fanny in order to avoid playing cards with the old ladies.

I find it actually a very funny scene, even if Fanny's feelings are again so overlooked.

But, I don't find her a typical girl. She's the one whose feelings are overlooked. I would be willing to bet that no man would have dared something of that nature with one of the Bertram sisters (or one of the other girls).