What are the essential symbols in the novel and what do they represent?
There are many symbols in the novel, and I think they are all essential. For instance, Randy's binoculars in the beginning of the novel represent his carefree life. He lazes around and uses these binoculars to watch birds, although his neighbor, Florence, thinks he's looking at her. Her opinion of him together with his lifestyle help represent Randy's life before responsiblity hits him like a ton of bricks.
Another symbol is Dan's doctor bag. It is referenced many times in the novel and it represents many things: Dan's profession, and the meds it holds which are helpful to the sick but necessary to those who are addicts. Later in the novel, it is stolen when Dan is ambushed and all the morphine and other meds he used to help the sick and injured is stolen by addicts and highwaymen.
The Model T is another symbol. It represents freedom and a way of life after the bombs. Without it, Dan would not have a way to get to the sick and injured, and the batteries they use to power the Admiral's ham radio would not be recharged. When Dan is ambushed, the car is one of the things the highwaymen steal, thus leaving the folks at Fort Repose in radio darkness and with a seriously injured and hindered doctor.
The Artesian Well is a symbol. It can also represent many things. This is the water that the Henrys have always used--it's free, it tastes fine, but it smells since it has a sulfur and heavy mineral odor to it. This water is not the first choice of Randy and others in the neighborhood due to the smell. So, consequently the artesian well could represent the prejudice and racial tension that is evident in the book. Water, also, is necessary for life. Working together--regardless of race, gender, religion, or other factors--is essential for survival in a catastrophe such as nuclear war.