yes, you can visit doha anytime as long as you are an engineer visa holder..just get an exit re-entry from saudi and off you go...you can visit by land or air...if land, you can get your tourist visa in the immigration and if by air in the airport..just provide yourself with a credit card since they won't accept cash...

in addition, it takes 3 hours from khobar to hofuf(immigration) from the border one hour to the city...if you will take the land...

enjoy your visit...