Dogs are a major predator in the US. The worst of it is they kill for fun, and will kill many at once, rather than just taking one or two for a meal. If your chickens can get high enough to avoid them, you will probably do pretty well without a coop. Chickens can and do find places to nest, but they are almost always on the ground. When nesting, they are likely to stay on the nest to protect their eggs or chicks, so are at even more risk from dogs. Perhaps you could set up a raised, sheltered area for setting eggs and raising chicks. You might find centrarchid's posts quite informative!
You could set up a roof and single wall of some sort, as shelter from weather if they want it, with nest boxes under the shelter. You will have a hard time finding eggs if they don't lay in a nest. This could also be a place to keep their feed out of the weather.