Getting To The Taj Mahal
That's exactly the way I did it. Works perfectly. The train you should take from Delhi to and back is the (the chair car is pretty comfy).
Getting From Delhi To The Taj Mahal
Leaves at 6.15 a.m. And gets to Agra at about 8.30 or so. You have all day and then you get the same train on its return journey. Leaves Agra at about 7 or so in the evening. Train numbers 2001 and 2002. For e-tickets, go to www.irctc.co.in. Incidentally, apart from the obvious, the other monument worth a visit is the Agra Fort.
Qutub Minar
I found that fascinating as well. If you take the 6:15 a.m. Shatabdi to, you will be there at 8:15 and you will be able to see the Taj by say 11:30 a.m. Then lunch at Agra and you can leave by 12:30 p.m. You will be able to reach Delhi airport for certain by 7:00 p.m. (accounting for evening traffic). 