Unfortunately, exertional headache can be benign; perhaps even hereditary in terms of migraine which may be noted somewhere in the family history. Because it sounds like you may be limiting your activities from the headache, I would have thought you'd be put on a trial with an anti-inflammatory, maybe aspirin or indomethacin (as mentioned by Bubbletrubble). But otherwise, I understand your doctor's position which is basically wait-and-see. Not only can this sometimes be an important diagnostic tool but often, it can be the only justifiable action based on the available evidence -- "Do no harm", that kind of thing. In the real world, one must constantly strike a balance between digging for an answer and the cost of digging; cost is not only financial, but also in terms of available resources, and the inconvenience, pain, and risk to the patient. Often, this equation is not an easy one, especially when held up against today's expections of knowledge and technology.
It's good that the scans were clear. (If you're uncomfortable with that conclusion, you certainly should get a second opinion.) At least, some serious possibilities have moved down the list. Further, your stess-test was apparently normal up until it was prematurely stopped. As such, it would seem that your blood pressure and (electrical view of the) heart was adapting normally to the increased exertion from baseline. This in turn can suggest that a number of other systems (blood, hormones, nerves) were probably operating normally up until the test was called off.*
IMO, so far what's been unaccounted for is the breathlessness you reported. How much of a factor was this in canceling the test? After the test was stopped, did you recover as expected; i.e. the staff made no comments and you walked out in a timely way, feeling as well as you did coming in? Do you notice this when carrying your dog upstairs or with other activities? If breathlessness is definitely a concomitant problem and you're starting to limit your activities because of it, it may be enough to justify something like a metabolic exercise test which looks at a bigger picture than a cardiac stress test.
* Your comment about your dog rang a bell about a very close friend who's a cardiologist who made the same complaint about carrying his daughter; but lightheaded instead of a headache. When his practice partner checked him the next day, he was immediately admitted for a CABG with a 99% blockage. This rang another bell: I'm aware of a very very rare condition called "cardiac cephalalgia" in which a migraine-like headache results from ischemic heart events aggravated by exercise. The theory is that a vagal nerve pain signal from the heart crosses over to the facial/head (trigeminal) nerve. It may occur despite clear cardiac stress tests and heart enzymes. A coronary angiogram may reveal an abnormality. But I underscore that AFAIK this is an exceedingly rare condition and I'm way way out of my sandbox on this. Maybe debersole can comment.