The pilot reported he was on a local personal flight with his two dogs, when he saw smoke coming up through the airplanes floorboards. He opened the side window so he could see and breathe better, but the increased air flow made the smoke worse. He made a forced landing in brush, and was able to exit the airplane and get his dogs away from the airplane before it was consumed by fire. The pilot said he was not aware of what initiated the fire, but believes it may have originated near the battery. Due to the remote location, the airplane was not examined by either NTSB or FAA personnel.