In Toronto we have a running joke that there are only two seasons in Toronto: winter and construction. Well, in Doha there is only one season - construction. The speed and extent of construction is mind boggling to someone who is used to construction in Toronto or Ottawa, in the latter of which it took nearly three years to add an extra lane to a highway (and only for a dozen kilometers or so!). Of course the speed and extent of construction isn't necessarily a good thing. Yesterday's road could be today's ditch and tomorrow's concrete barricade. You just never know and no advance warning is given! There's a reason why Doha cabbies often have the vaguest notion of how to get you where you need to be: roads might be blocked or simply disappear overnight, many streets (especially in the suburbs) do not even have names or lack road signs, and then of course there's Doha traffic.
To be honest, drivers in Doha are not that bad. Yes, they tailgate, cut into traffic, and use horn as the primary means of communication. On the other hand they are careful around pedestrians, stop on a red light or a stop sign, and signal a turn fairly often (although nor reliably so). The only times to really beware traffic are between 6 and 8 in the morning when everyone is dropping kids off at school and heading to work, and between 6 and 8 in the evening when everyone is out and about shopping or heading to work. The city streets become an unending stream of light and noise after dark. But of course it's never fully dark as the city's glow is reflected from the cloud of smog. Resting workers on the rare patches of grass after dark, parked cars, teeming shops small and big, neon ads all whiz by as the vehicle swerves and turns on roundabouts and u-turns, only to suddenly plunge into narrow black alleys to avoid the busiest thoroughfares. Arabic, English, Tagalog, Urdu, Hindi and other languages figure prominently into the city's spoken and written landscape, but the horn is the universal communicator. Very short single burst to thank someone or to let them know that you're right behind them. Slightly longer honk to catch attention and make sure that they see you cut in in front of them. Long indignant blare is for someone who is taking too long to park or leave a parking spot or who cuts in and then immediately brakes. The greatest hazards are brief sandstorms that can drastically reduce visibility, and the native Qatari drivers. The latter all love huge American 4x4 off-road vehicles and when faced with traffic they simply take to the big empty spaces on the side of many roads (filled with sharp rocks and sand) and simply gun it only to aggressively cut back in further ahead. Few non-Qatari drivers attempt this maneuver, although most drivers might cut corners using the road's shoulder.
The car or a mini-bus is the primary way of getting around Doha. The public transportation is nearly non-existent. The official seafoam-green city cabs are especially thick on major arteries, downtown and the airport, but there are plenty of private drivers hassling would-be riders outside of shopping malls and large stores. Those are to be avoided as they do not have meters and usually ask for far too much. Even when getting a city cab it is best to insist immediately that the driver turn on the meter, as stories of people getting ripped off by cabbies are in the top 5 bitching sessions (heat, traffic, exchange rates, and price of alcohol usually being the other four). However, if you know how much a city cab or an Uber ride would charge for the distance you could haggle with the private drivers and save a bit of money. An Uber is really the best option short of renting a car or relying on a friend who has a car. Uber drivers usually stick to the prescribed route and rarely have a problem finding where you are to be picked up (a problem I ran into when trying to order a city cab). A ride from out in the suburban boonies to the heart of downtown only set me back 44 QR (12 USD), and a city cab was comparable in price.
Oh, and of course the other important thing to note about Doha roads are the speed humps.