Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Doha to Quetta as you normally would.
Expected rainfall in Doha is more than in Quetta. You can expect this to be the case over the next 5 days.
You can imagine temperatures to be in the 42 °C range in June. The weather in Quetta is generally colder than Doha's. As flight availability is subject to become more limited as peak season approaches it is ideal to book in a timely manner.