I’ve seen the comparison and contrast of Lewis Carroll’s Alice to L. Frank Baum’s Dorothy Gale covered many times, on the Royal Blog of Oz, for instance. I believe Baum admitted to being inspired by Alice in creating his own heroine, in that she was someone with whom children could identify. I recently took a look at Mari Ness’s reviews of Alice’s Adventures in Wonderland and Through the Looking-Glass, and there was some argument over how bland Alice is. I guess this could have to do with the idea that the protagonist can be a stand-in for the reader, and hence perhaps a personality all that well-defined could ruin this. Both Alice and Dorothy were normal children visiting a weird world, but that certainly doesn’t mean either one was purely passive. Both were generally friendly and polite, fairly stoic in the course of their adventures, yet certainly capable of losing their tempers and standing up to danger. Dorothy’s anger leads her to slap a lion and inadvertently kill a witch, while Alice’s manifests itself most clearly at the ends of her two books. It’s also notable that neither one starts out with a desire for adventure, something that was changed in some of the better-known film adaptations. They do both develop more of a taste for fantasy adventures in their second outings, and while we don’t know what happens to Alice after this, Dorothy eventually becomes a seasoned traveler who’s always wandering into unknown territory.
I think one of the more significant differences between the two heroines is, as Jared Davis mentions, Dorothy’s family is poor, while Alice’s comes across as fairly well-to-do. This isn’t specifically stated in the latter case, and I believe the time and place in which Carroll wrote was one in which it was common for middle-class families to have servants, but even middle-class is better off economically than Dorothy’s situation in Kansas. Alice Liddell, who was in some ways inspiration for the character of Alice, was the daughter of the Dean at Christ Church in Oxford; but there’s some debate over how much of Liddell’s home life we can extrapolate onto the fictional Alice’s. Still, we know she has a governess, and at one point bemoans that she might have turned into her poorer acquaintance Mabel. I can’t remember for sure, but I believe I found Alice quite well-educated for a seven-year-old when I read the books as a kid. Then again, that might have something to do with differences between nations and social classes, particularly regarding the fact that she’s already learned some French. We Americans are known for being particularly ignorant when it comes to foreign languages, and for that matter our own language. She’s also acquainted with social etiquette and pretty good at reasoning, her difficulties in Wonderland and Looking-Glass Land being due largely to the inhabitants’ rudeness and nonsense. And her getting times tables and the words to poems wrong might well be due more to the nature of her dream than to ignorance on her part. She doesn’t appear to know how long ago William the Conqueror lived and isn’t familiar with the concept of negative numbers, but she IS only seven.
As I stated here, Dorothy’s age at the time of The Wonderful Wizard of Oz, or for that matter in later books, is never specifically stated. I tend to think she’s maybe around eight when she first visits Oz and eleven when she moves there, but that’s hardly set in stone. She can read at the time of her first visit, which suggests but doesn’t require that she’s started school. She doesn’t know where Kansas is, but is aware that it isn’t that far from Omaha. In later books, she’s more knowledgeable about geography, at least partially because she’s traveled in the mundane world as well as the fairy one. There’s a passage in Ruth Plumly Thompson’s Grampa in Oz that could be taken as an indication that Dorothy isn’t good at arithmetic, but it’s honestly a bit confusing. She says that six and one are eight, but is this a mistake on the character’s or the author’s part? The Oz books were never all that carefully edited.
One noteworthy aspect of Alice’s personality is that she comes across as rather lonely. As Mari writes about Looking-Glass, “Alice’s initial companions are Dinah, her cat, too busy washing kittens to pay much attention to Alice, and a black kitten. The text tells us that her sister and her nurse don’t like Alice’s games of Let’s Pretend, and also that Alice plays chess with herself—pretending that her kitten is playing on the other side.” She frequently talks to and even punishes herself. Dorothy also appears to lead a rather solitary life, as the farm where she lives is far out in the country, and as of Wizard her aunt and uncle are too busy to spend much time with her. There’s no mention of her having any friends at school. She makes friends easily while on her travels, however, and later grows closer to her relatives. Of course, the inhabitants of Oz are usually friendlier than those in Wonderland. Dorothy occasionally shows pride in being American, as when insisting that Princess Langwidere and the Dragonettes treat her as an equal. While Alice’s Englishness is a significant part of her character, she doesn’t have much of an issue speaking her mind to kings and queens. She DOES become a queen herself near the end of Looking-Glass, as Dorothy is made a princess by Ozma. Overall, I have to say I’m a bigger fan of Dorothy, but then she DOES appear in a lot more books, so it’s not an entirely fair judgment. Alice strikes me as a little more stuck-up, but I think that has a lot to do with her upbringing.