Ever heard of the five stages of grief? At Agatha's funeral, Georgie gets stuck on stage one—denial—and won't let go; she says, "it was the day of my sister's first funeral and I knew it wasn't her last—which is why I left" (1.1). And it's a good thing, too, since Georgie's refusal to accept her sister's death despite all the evidence drives the whole story.
Of course, Georgie turns out to be right because Agatha's not dead, but this isn't the only time we see Georgie close her eyes to what's right in front of her, especially when it comes to her sister. Months before Agatha's disappearance, Georgie insists that Agatha is going to stay in Placid and run the store with her, when it's clear Agatha has no intention of doing that. She's either going to marry Billy and go to Minnesota, marry Mr. Olmstead and spend all her time in his library, or go off to college.
Later, Georgie refuses to see that Agatha and Billy really have gone their separate ways and that Agatha actually does dig Mr. Olmstead. A key part of Georgie's internal journey, then, is learning to accept that Agatha will eventually leave her.
After her shootout with the Garrow Gang, a newspaper describes Georgie as "a pigtailed hoyden" (21.3). While we in the 21st century are perhaps a bit more enlightened in terms of what constitutes masculine versus feminine behavior, in 1871, Georgie certainly would have been described as a tomboy given her penchant for hunting pigeons and her fondness for her gun and running the store accounts. She even changes her name to make it more masculine. She explains:
Have I mentioned my full name? It's Georgina Louise Burkhardt. Now, Georgina doesn't suit me—it's the kind of name that has daisies growing out of it. But Georgie is fine by me and fine by everyone else, too. (4.23)
Georgie may be considered a tomboy, but it's not like anyone in the Wild West town of Placid is exactly a girly-girl. While Georgie's behavior sometimes gets on Ma's and Agatha's nerves, that's more because Georgie acts exactly like Grandfather Bolte than because they consider her behavior masculine.
Ma runs the store right along with her father (or, you know, under her father disappeared), and Agatha is known for leading sightseeing hikes and sometimes camping out alone all night. So it's not as though either of them is really set on staying inside and keeping her manicure perfect—they just don't like Georgie's hunting, Ma because it makes a mess and Agatha because animals die for no reason.
Georgie is a homebody when it comes down to it. Her goal is to grow up, live in Placid, and inherit her family's general store. She doesn't want to be anywhere else, and she doesn't understand why Agatha needs to roam. She describes the difference between them this way:
Feathers claw their way back into the sky, whereas leaves, after flying once, are content to rest on the earth. Agatha? She was a feather. She pushed higher, farther always. I suspected my constitution was more leaf than feather. I hoped I was wrong about that, though, because I wanted to be like Agatha. (3.2)
Georgie isn't wrong. Later, after she returns home, she thinks, "I heard the sounds of my neighbors. I would be part of them tomorrow. Then I thought: I am part of them. They know I am here. I was home" (20.70-72).By the end, Georgie accepts that it's her nature to be a leaf, just as it is Agatha's to be a feather.
When we consider that it's Georgie's nature to want to stay home, we have to point out that her trip to Dog Hollow and beyond takes her far out of her comfort zone. She never actually comes out and says that a road trip is out of her element, but we can infer that it is from the way she describes herself. That this doesn't stop her, though, makes it all the more touching that she ventured out to find out the truth of what happened to Agatha. No one backed her, and trips aren't really her thing, but Georgie fearlessly trekked off anyway. Lucky, Agatha.