Okay, so we're not exactly talking poverty on a Charles Dickens level, but this family sure doesn't have much. What's weird is that, in Where the Red Fern Grows, poverty ends up seeming like a blessing. Poverty lets Billy grow up in an idyllic pastoral forest; poverty gives Billy the opportunity to learn all about hard work while figuring out how to get his dogs. Lucky him!
The novel depicts poverty positively, because it allows Billy to stay in the country longer and hunt with his dogs.
Billy's poverty makes him a more sympathetic character. Without it, we wouldn't be so interested in him.