As the oldest Alden gal, Jessie is a nurturing sister who spends most of her time looking after the younger kids and Watch the dog. Like magic, she knows how to cook any sort of food you put in front of her, and the way she keeps house would make Martha Stewart proud. Whether she's making stew, rigging up a line for the washing, or scavenging dishes from the local dump, her combination of know-how and a willingness to make do with what she has serves her family well.
Jessie is resourceful and observant, with superior powers of deduction. When the kids are looking for a place to sleep, she says, "This is a good place. It is far away from people. You can tell that by the grass in the road" (2.58). Though Henry is the "smart" one—to his credit, he's the one who discovers that Mr. Alden is their grandfather—a close read suggests that Jessie is the more observant of the two. After all, Henry meets Mr. Alden on Field Day, but he doesn't recognize him later in the book. We're thinking Jessie totally would have, though—she pays close attention.
As the housekeeper, cook, and babysitter, Jessie is the family's maternal figure, forming a pseudo parental unit with Henry. When there's a problem, Henry consults with Jessie first: "Do you think it's all right, Jessie, to build the dam for a swimming pool on Sunday?" (7.81), he asks. The "parents" never seek input from the younger kids, and often they keep secrets from them. It's worth noting, though, that Jessie seems more open with other people than her big brother. When Dr. Moore asks about the children's parents, Henry is silent but Jessie offers, "Our mother and father are dead" (9.20). It's unclear whether she's more trusting than her brother or just a better judge of character—perhaps it's both.
Though Jessie's femininity is emphasized through her role in the family—a role that reflects common gender roles at the time the book was written—we also know that she has initiative and survival skills. She's the one who finds the boxcar in the first place, and though Benny takes credit for it, we can assume she also plays the lead role in building the family's fireplace while Henry is at work:
The fireplace was a very good one. The children and Watch had made a hole at the foot of a big rock between two trees. Flat stones were laid on the floor of this hole and around the sides. More big stones were put up to keep out the wind. (7.34)
That doesn't exactly sound like the work of a 5-year-old, does it? There's no way Jessie doesn't mastermind this, though she's supportive enough of her youngest sibling to let him take the credit.