Nowadays most young ladies of Miss Darcy's age would bristle at the word 'obey.' It says a lot about the times we live in, doesn't it? ;)

I think this passage shows us that Miss Darcy was inexperienced when it came to inviting acquaintances to her home and probably in other things as well. This is also the first time that we see Georgiana and this shows that she does obey, a practice that can be positive given that Darcy is her older brother. He seems to care for her very much. Seniority, familial relations and (ahem) gender mattered more during those times, IMHO.