When travelling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Alice Springs is roughly similar to Cairo. You can assume this to be the case over the next 4 days.
Expect the weather to be around 37 °C on average in January. As the temperature peaks, try to get your plans done early, as flight price and availability will have an impact on your travels. The climate in Cairo is generally colder than in Alice Springs.