I just returned from a weekend at a family members mountain home. The house sits at 9958' ASL. This is based on several Garmin GPS readings and on USGS maps.
My H successfully launched and flew at this altitude. It even flew as high as ~10,150' ASL. My H did not require any special firmware. It is using the current firmware available to all.
At that altitude, you could hear the motors working harder to keep it aloft. Everything reacted slower due to the thinner air. Had to be careful descending and moving in the X axis as it took it longer to slow/stop. Battery life was definitely shorter. I didn't time it, but I know based on previous flights. I played it safe and brought it back closer to me when the battery got to 14.9 volts. The motors were not any warmer/hotter than normal...
Again, the H took off and flew above 8,000' ASL with no special firmware like the Q500...
BTW, I live at about 6,000' ASL and regularly fly at this altitude with no issues. Even flying at 8,000' ASL, I've not noticed any significant differences, but at that 10k mark, handling is noticeably different.