As far as I know, taxis take only cash. There are ATMs and money changers in the terminal. There is also an ATM in the corner of the W lobby.

Taxis are inexpensive and Doha is not very large (although congested at peak times). The fare is usually about QR 50 (US $14) to the W hotel (including the recently raised airport surcharge).

On the way back there are no public taxis at the W hotel but you or the doorman might be able to call one. They have hotel cars, which are likely several times more expensive (the minimum hotel car to the airport may be QR 150 according to their website). I use local private drivers from a company and their standard charge is QR 50 to or from the airport (plus waiting time if needed at QR 30 per half hour). If you PM me, I'll send you my guy's name and local number.

I usually tip taxi and car drivers in Doha although I can tell you many people do not.