What is your specialization as a civil engineer? What is the category of your experience.. There are so many fields that a civil engineer can work. Design and detailed engineering? Site surpervision? QA/QC ?  Planning and scheduling? Costing and budgetting? Project management? Based on this categories,  the speed of processing of your working visa will depend. If the company hiring you, needs your specialization very quickly then your visa might be procesed faster..
One thing though that i can say is that (based on my observation around doha) There are so many construction works going on around Qatar, in all categories. My company even has a lot of projects that we are coming short of manpower.. DOnt worry about who will process your visa since your company will  take care of that. Good luck..