My views on your being a woman have little to do with why I don't recommend hiking Whitney alone. You'd be hard pressed to find a time during the summer to hike that trail where you'd actually be "alone."
But much like Akichow said, just having someone that hikes with you and knows you and might be able to see the signs of AMS should you encounter them can be very, very important. The first time I hiked Whitney alone, I made some very serious mistakes involving AMS and almost wound up paying a very high price. The last time I hiked Whitney, a good friend of mine wound up with signs of AMS, but wouldn't have said a word about it and kept hiking onward and upward had I not noticed some pretty obvious differences in his hiking and his general demeanor.
So it's absolutely doable. But it's much safer if you can find someone else to hike with.
