When flying from Dubai to Port Moresby, the time of day you decide to fly out makes little to no difference towards the overall price you’ll pay on tickets.
When travelling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Dubai is roughly less than Port Moresby. You can assume this to be the case over the next 5 days.
Expect the weather to be around 41 °C on average in July. 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 Port Moresby is generally colder than in Dubai.