Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Doha to Galway as you normally would.
For a flight from Doha to Galway, you will be flying from Hamad Intl. Doha Hamad Intl (DOH) is just 8.8 km from the centre of the city. Hamad Intl is the only Doha airport and it handles 0 outbound flights to Galway per day. 0 airlines have flights to Galway from Doha Hamad Intl on a regular basis.