Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Doha to Funchal as you normally would.
Expected rainfall in Doha is more than in Funchal. You can expect this to be the case over the next 5 days.
With an average temperature of 42 °C, peak weather can be found in June. As a traveller, expect to see changes in flight prices during that period. The temperatures in Funchal are colder than in Doha.