There are many large villas and houses available for rent within 45 mins of the airport. Everywhere in Doha is within 45 mins of the airport. Unlike most cities, the airport here is actually in the city itself.

As to cost, there is a huge variety of standards and range of properties and prices. But broadly speaking I would guess you are looking at around QR15,000 per month.

Cost of living? Its many years since I lived in the UK but I would think it is broadly comparable but slightly cheaper here.