Coming from the UK, we have the National Health Service so generally we do not have to pay for medical treatment or maybe a small fee.
As I understand it, in Qatar there is a public medical service and you can go to the Hamad Hospital. My wife has been there once for an out patients visit and this was pretty efficient (although the separation of the sexes was in place) and the prescription charge was on 2 Riyals.
However if you want the flexibility and comfort of more choice then please do some research on medical insurance if your company does not provide it for you. If you are from overseas and not used to the climate etc then you are at a higher risk than if you are in your home country. Also, your family too must be considered, a family policy should be purchased.
Check the cover very carefully to ensure that you know what you are covered for and what you are paying for. Monthly payments are usually allowed too.
I have cover through my company with Allianz and they have an office on the C Road down from Ramada Junction towards the airport, but there are obvioulsy other providers so please check them out.