Character Analysis
Brownie
Brownie is J.D.'s dog: "Brownie was the only dog we had ever owned who wasn't a mongrel. He was a purebred Alaskan" (3.1). Brownie's purebred status means he's desirable dating material, so Tom works out a plan to mate him to the Jensens' dog, Lady, and sell the puppies as prime sheepdogs.
Brownie's not just a pretty face, though, and he also plays a key role in Tom's plan to rescue the Jensen brothers and Lady from Skeleton Cave. Brownie is a great example of how Tom's schemes tend to benefit others while really benefitting Tom himself. J.D. gets a great puppy out of the deal, and the Jensen brothers get rescued and sell their puppies for a silver dollar each. However, there's just something about Tom's schemes that's not quite right, though like J.D., we can't ever prove it.
Dusty
Dusty is Sweyn's mustang. He plays a role in Andy Anderson's plan to kill himself, mainly by not complying, which is a good thing for Andy in the long run:
Dusty turned slowly around so Andy wouldn't fall off. He grabbed my cap out of my hand with his teeth. He dropped the cap by his forelegs and put a hoof on it. Then he twisted his head and rubbed his nose against Andy's good leg. (8.158)
Tom walks in on this scene and takes on the task of rehabilitating Andy, which in turn leads to his own reformation.
Lady
Lady is "the first dog that Brownie didn't chase away when she came near him" (3.3), so she's the lucky lady J.D. mates his pup with. First, though, she gets lost in Skeleton Cave with the Jensen brothers. Because she's in heat, Tom is able to use her scent to get Brownie to track her in the cave. You go, girl.