16K should be enough. Firstly the best thing to do would be getting a shared villa with other co-workers or your looking to spending a good 6-8k just on decent studio accomodation, with a shared villa you could be looking at only spending 2-5k each, the downside being you have to live with 3 or 4 others.

With your travel allowance you will be up to QR17,625 which is good, I would recommend you rent a car for the first year, that will set you back anywhere between QR1.5k and QR4K a month depending on what car you want, petrol is cheap you'll probably spend about QR200-300 a month on that, if your driving on city roads then I recommend a 2WD, make sure its automatic as you dont want to be stuck in long ques of traffic jamming the clutch down every few seconds as you inch forward. I would look into getting a second hand 4WD after a year with your savings if your here for the long term, anything by nissan, toyota, or mitsubishi is the way to go, reliable, and parts are cheap. Dont go for european or american cars unless you are prepared to pay an arm and a leg for parts, apart from maybe GMC which are reasonable.

Health care wise you can get the company to provide you with the bare essential health card (costs around QR100 I believe) which allows you to use the public hospital, however it would be wise to ask for full health insurance in order to use private hospitals such as Al Ali which are a lot nicer (go there without insurance and you will literally be paying thousands just for a simple check up).

Now the major question is how often do you drink alcohol and eat out. The average cost of a pint here is about 6 british pounds, spirits are ridiculously overpriced, go to any hotel club and they will be charging you a minimum of 80 pounds for a bottle of cheap voddy, go out for a big one and your looking at spending over QR500 easy. Food is also overpriced, if your looking at eating out daily you will probably spend over QR 500 a week on food.

As for internet they are currently installing fibreoptic cables around Doha but will probably take atleast a couple of years before they become fully functional, for now your looking at spending around 500 riyals a month just for 8 meg internet, I would suggest going with the phone/internet/tv option for around 250 a month which is only 2 meg but the savings are big.

If you want to know anything else let me know.