It seems to be possible to be in a conscious state without consciously thinking about anything at all. Presumably consciousness is created by a subconscious process. I can't say much more than that it's possible for information-processing systems (such as the human brain) to be conscious. My guess is that consciousness is a non-physical, emergent property, that only exists while a certain component of the information processing system is operating in a particular way.

Yeah, I think it has something to do with a brain that has enough complexity that it can begin to model itself and others' brains, allowing self reflection.

A dog can think, I think, but I don't think it can think about its own thoughts. But this may be unknowable.