To my knowledge, Umrah visa is restricted to Makkah and Medinah. I am saying this because during my last visit an Indonesian lady on Umrah visa was trying to buy a bus ticket in Medinah to go to Dammam as she wished to visit her relative. She was denied the ticket by Saudi Public Transport Company (SAPTCO) and was told she is not allowed to travel to any other city. However, I suggest you check with Hajj & Umrah travel agencies in Doha, and they may be able to guide you on this.