Maybe I have this wrong. I didn't think the time was really relevant. I can burst into very active cardiovascular exercises and achieve 180-190 bpm in around 10 seconds quite easily. If I go for a walk on a flat surface, I will never achieve more than 100 bpm. It usually goes to 100 for about 5 mins then goes back to 90. If I walk up gentle inclines, I will see it rise to 120-140 and then after about 5 mins drop down to around 110-115. If I walk fast up an incline then I can obviously push my rate up, usually to 140-160 and it stays there. What can be an indication of fitness also is how quick the heart recovers. When I stop exercising when peaking 190, after about 2 mins it slows down to 90 and stays there for about 10 further mins before dropping to its usual 65-68.
I think what is most important in a stress test, is evaluating how hard your heart can work before problems occur, and identifying those problems. It is also important that you CAN reach your optimum, or there is definitely something amiss. I had no idea it was on a time based thing, to me that would be like a race. Every stress test I've had, the operator has always said "ok I will now speed it up a bit more" or "It will now increase in incline". He never seemed to watch the clock or keep to a specific time schedule. My first stress test was a disaster, I lasted 9 minutes but was short of my optimum. They were surprised I had chest pains because nothing out of the ordinary was showing up.
My first stress test at your age lasted about five minutes and problems were determined, the test stopped and I went straight to the hospital. Two years later I went 12 minutes before reaching my optimum heart rate, and six months or so later I lasted a very few minutes...
I think your physical condition, heart and lung health and other factors have a whole lot to do with how long a stress test lasts. I'd feel really good about going 10 -11 minutes. Hope it turns out well, keep us informed.