I'm looking for the title to a book I read in the 80's about a family set in the present day surviving after a nuclear holocaust. The whole family survives for a time. The little girl hides under a table and suffers less radiation sickness than her family. Eventually the survivors emerge from hiding and start a new society, but they don't live long because of radiation sickness. It was a terrifying young adult novel.
Children of the Dust. The book details three generations of a family during the aftermath of a nuclear war. The survivors of the blast suffer through radiation, nuclear winter, feuds between rival groups and radiation-induced mutations, eventually evolving into a new species, Homo superior. The new species has adapted to the loss of the ozone layer and the abundant radiation, and will become the dominant species on the planet.
Catherine. Catherine is known by three names. Catherine, Kate then Old Kate. Catherine was her first name. She was eight as she lived under the table in the living room while there was the fall of nuclear dust.
Are you certain it was a novel, or could it have been a novelization of a movie? The most famous post-nuclear attack movie of the 80's involving families was The Day After. While reading your question I immediately settled on the memory of Steve Guttenberg carrying a little girl's body out of their last refuge. Also starred Jobeth Williams and Jason Robards. It was a big deal, a multiday television event that sparked much political notice and debate. Wikipedia says there were viewers guides distributed to schools; I'm sure the movie would have followed with a book.
I believe the answer is Brother in the Land. This story is similar to your memory, it was also read in a lot of school classrooms in the 1980s. It has to be the bleakest children's book ever written.
Denny, a teenager, is one of the unlucky ones, a survivor, one of those who have come through a nuclear war alive. In plain language he sets down all that has happened to him, what he sees, and what he feels in the first days after the bomb has dropped. This novel won The Other Award for 1984.
It only covers a single generation, with the 1994 reprint revealing that one of the females is pregnant courtesy of one of the male protagonists after two of them die, one explicitly of radiation sickness.
There is a children's book called "Outside" that also might be relevant to your question.