I have never been hiking at altitude before.
It’s your lack of high-altitude experience, not your itinerary, that concerns me. Some people would do just fine with your plan. Others would get deathly sick and find themselves unable to descend. Most people fall between those extremes. I would spend a night at Horseshoe Meadow. If you feel fine the next morning, you’re probably OK. If not, I wouldn’t risk being 13 miles from my car when I got worse.
I would also get a prescription for Diamox. Most people start taking it at least a day before going to altitude, but it will help if you wait to see how you do and take if/when symptoms develop. These are several threads that discuss altitude issues. Read all that you can.
