Is there any significant narrative reason for Dorothy to be an orphan living with her aunt and uncle? It's often the case that someone not living with their parents leads to a later reveal, about how they're the child of a god, royalty, great wizards, or a Dark Lord of the Sith. While we do see this motif used in the Oz books, as with Tip/Ozma and a whole bunch of Ruth Plumly Thompson's characters, no such information is forthcoming about Dorothy. In fact, all we learn about her parents appears in a single statement in The Emerald City of Oz: "As for Uncle Henry, he thought his little niece merely a dreamer, as her dead mother had been." So Henry knew her mother, but we don't know whether he was related to her or to Dorothy's father. Another literary reason for someone living with people other than biological parents is based on the idea that people don't provide the same kind of love for kids they didn't contribute in creating. Some people even seem to believe this in real life, which I think is hogwash, but it can be a convenient shorthand in fiction. Caretakers who aren't parents can be well-meaning but misguided (Luke Skywalker's Uncle Owen and Aunt Beru), abusive (the Dursleys in the Harry Potter series), or even downright vindictive (Vasilisa's stepmother in the Russian fairy tale). It seems to me that L. Frank Baum originally presented Dorothy's caretakers in the well-meaning but distant category, as suggested in the description in Wonderful Wizard:
When Aunt Em came there to live she was a young, pretty wife. The sun and wind had changed her, too. They had taken the sparkle from her eyes and left them a sober gray; they had taken the red from her cheeks and lips, and they were gray also. She was thin and gaunt, and never smiled now. When Dorothy, who was an orphan, first came to her, Aunt Em had been so startled by the child's laughter that she would scream and press her hand upon her heart whenever Dorothy's merry voice reached her ears; and she still looked at the little girl with wonder that she could find anything to laugh at.
Uncle Henry never laughed. He worked hard from morning till night and did not know what joy was. He was gray also, from his long beard to his rough boots, and he looked stern and solemn, and rarely spoke.
Dorothy initially appears to be closer to Em, as evidenced by her telling the Silver Shoes, "Take me home to Aunt Em!" When we see her again in Ozma,however, she's making a journey to Australia with Uncle Henry, and it looks like this brought the two of them closer together.
In later books, being an orphan is often a way for a character to come to live in Oz without leaving loved ones behind, as it is for Bob Up in Thompson's Cowardly Lion and Robin Brown in the McGraws' Merry Go Round. On the other hand, Speedy is described as an orphan and Peter Brown appears to be one as well, but they both have relatives they're loath to leave (an uncle in the former case and a grandfather in the latter). Trot and Button-Bright are weird in this respect, as they are both implied to come from two-parent households (well, Trot's father is away at sea, but apparently still alive), yet still come to Oz to live with no apparent consideration taken for grieving parents. And we know nothing at all about the parents or relatives of Betsy Bobbin or Jenny Jump. This is probably due to the fact that both were originally conceived of as adults (Betsy in the play on which Tik-Tok was based and Jenny in John R. Neill's original Wonder City manuscript), but how hard would it have been to have inserted a reference or two to their caretakers?