pretty open ended question with not much detail about your experience hiking alone or at altitude, or age for that matter.
Some things to think about when going alone:
- Are you used to hiking alone?
- have you done 15 miles or longer day hikes with moderate elevation gain(4k or more)
- how often have you been above 12k or 13k?
- the intense UVs and dry air really takes a toll on a body and most under estimate this coming from more humid environments
When I told my wife and family i was doing whitney alone they expressed some concern. Heck even I wasn't sure how I would react with that much distance and altitude gain once above 13k. But i've done enough long days 15-22 miles at altitudes between 10k-13k that i felt i knew how i would react and if it started going downhill then i'd know it and bail. I also do most of my hiking alone - on and off trail so felt pretty confident in doing whitney alone. Like others have mentioned, there will be a lot of people on the trail that time of year so it's not like hiking off trail alone in the backcountry.
good luck and have fun on your trip what ever you decide.