Visiting Egypt in the autumn sounds great as the weather is going to be quite warm.
I believe one day in Cairo is not enough as lots of highlights have to be explored like the Pyramids,Old Cairo, National Museums ... etc. Just try to cover as much as you can for this time and next time explore the rest.
Also for your information there is a direct flights from Doha to Luxor direct if you would like to start your trip from Luxor to Aswan and end it in Cairo to have more time.
The Cruise from Aswan to Luxor is going to be amazing as you will stop at each city to discover the famous temples like Isna, Idfu, Kom umbo temples and others.
Normally its safe to go around on foot if you wish you just need to take a good care of your staff not to forget it any where.
Wish you a memorable trip and looking forward to share your trip experience when you are back to Doha.