Read this excerpt from Through the Looking-Glass by Lewis Carroll. Alice did not like shaking hands with either of them first, for fear of hurting the other one's feelings; so, as the best way out of the difficulty, she took hold of both hands at once: the next moment they were dancing round in a ring. This seemed quite natural (she remembered afterwards), and she was not even surprised to hear music playing: it seemed to come from the tree under which they were dancing, and it was done (as well as she could make it out) by the branches rubbing one across the other, like fiddles and fiddle-sticks.

The details of this excerpt imply that

Alice likes to dance and often greets people in this way.
Alice is very uncomfortable when she meets the brothers.
Alice is overjoyed and wants to stay with her new friends forever.
Alice is becoming used to the unexpected in the looking-glass world.