You will be fine in terms of time. I would recommed coming back to Delhi for the night since you say you have to be at work the next day.
I'm sure you'd be fine if you rented a car from a reputed organization like Hertz. (Keep in mind that in India, Hertz cars come with drivers.)
https://www.hertz.com/rentacar/locat...ELT51&locType=
Fyi, keep in mind that the Taj Mahal is closed on Fridays.