Hi there and thanks for your question!
We don't really recommend using cedar chips for dog bedding. There are a few reasons for this.
Some dogs can be allergic to the chips. They can develop a contact allergy that causes skin problems. There is some fear that the residues exuded from the the cedar oils can cause liver problems.
Also, the cedar chips are the perfect size for a dog to swallow and have an intestinal obstruction.
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.
As long as your dog is not reacting to the hay (i.e. skin or inhalent allergies), hay is a great choice.
Recycled or shredded newspaper is not bad as well. It is also acceptable to have a large blanket available for the dog to lay on as well.