Best Answer - Chosen by Voters
That trip would take several days one-way on a boat, even if it is possible (I'm not sure but I think there might be cataracts in the river between luxor and Cairo).
The overnight train is an interesting trip, quite comfortable and it means you travel while you sleep, but maybe not advisable for a woman travelling alone (due to hassle, not danger).
I would definitely look for somewhere to stay overnight in Cairo or Alexandria. You will be really rushed to see much of either of those cities in one day. The traffic in Cairo makes it hard to get anywhere quickly. Personally I would choose either Cairo or Alexandria and stay overnight there, or if you really want to see them both, stay 2 or 3 nights.
2 weeks is actually a long time to stay in Luxor, you will be "templed out" after 1 week, so a couple of days in a city is a good idea.
Edit:
Another option might be to combine your hotel stay in Luxor with a boat cruise. The boats go from Luxor to Aswan, stopping at various places on the way. It's a great way to travel!
Source(s):
Been there, done that, bought the papyrus scroll :-)