When we first meet Sara, her clothes are quite fancy and sumptuous. There is a whole lot of emphasis on outward appearance, clothes and all the finery that comes with "good breeding" in A Little Princess. But despite what Miss Minchin and Lavinia think, they can't just strip away Sara's clothes and expect her to be a beggar or a scullery maid at heart. In fact, even when she's dressed in all rags, the children of a rich family recognize that she must not be a common beggar because of the way she speaks. So—appearances might count, but they sure aren't everything.
Though her appearance may change drastically in the book, Sara remains the same princess-like girl in spirit.
Even though Sara looks like a beggar girl, her actions make it obvious to people like the Large Family children and the bakery woman that she's more than that.