Collins is establishing here just how independent and cut off from her mother Katniss is. Not only is she the one putting food on the table, she is the primary caretaker for everyone in her family. She’ll later establish the same thing with Peeta and his abusive mother.
She is both showing the similarities and differences between Gale and Katniss here as well. Gale is lumped in with her as being the primary caretaker for his family, including his mother. However, as we learn in Catching Fire, Hazelle Hawthorne is a much more available mother to her children than Mrs. Everdeen is. The fact alone that she even gets a first name at all is evident of this. Gale is the one putting food on the table for his family, but he is not as cut off from them as Katniss sort of is now, and definitely will be down the road. When she comes out of the Games, the only person who will truly understand the experience she’s been through is fellow tribute, Peeta. Gale’s being closer to his family than Katniss is symbolic of this.
We also see the first discussion of Katniss’s feelings about having children. She doesn’t want them. But the previous paragraph has just set her up as being a natural mother — she is both protective and caring for her younger sister. It isn’t that she doesn’t like children, it’s that she’s afraid of the pain of losing them. It’s the beginning of her character arc. Katniss is a closed off person who needs to learn to open up to love. It’s symbolic of Panem needing to learn to open itself up to a more humane society.