welcome to doha ... as oryx pointed out always carry a mobile and call 999 for help when in problem ... i got a wrong call (full pf filth) while at work and i called 999 and reported them the number ... they called m,e back in 15 minutes time and told me that it was from a public booth in al rayyan area and asked me not to worry cos they will track my calls for next few days ... well after that i didnt get any such experience again ....
people try to follow you ,sometimes stop near u and offer a lift just ignore ... well all such things can happen anywhere ... as per me doha is a far more safer place than India in regard for safety of ladies...