Dear Job and Visa:
The H4 visa, issued to the spouse and dependent children of an H1 visa (temporary work visa) holder, does not permit the H4 visa holder to gain employment in the US. You can not work, temporarily or otherwise, in the US as an H4 visa holder. We assume that you knew of the restrictions on your H4 visa status, prior to accepting them as the conditions for your entry into the US.
Despite the conditions of your current visa, the US INS (Immigration & Naturalization Service) allows you to change your mind and seek ways to change your status, and thus your quest for the H1 visa. Since you have the H4 already - and your spouse must have obtained the H1 - you know the process for obtaining the H1 better than most people. You must find an employer who is willing to sponsor you for the H1 visa.
Employers in the US typically recruit temporary foreign workers only when they can not find qualified local citizens or permanent residents. The reason is simple: The process for obtaining an H1 for a prospective employee is both time and resource consuming. Since we have not heard of a serious shortage of civil engineers in the local market, your task of searching for an employer for obtaining the H1 visa is likely to be an uphill task. We think it is unlikely that any one state in the US has more demand for civil engineers than does any other state.
Searching for a job in your case is no different from how your spouse obtained a job, or how others would go about finding a job in the US or anywhere else in the world. You can use the network of personal contacts, newspaper classifieds, websites, and so on. One place to start is the
iMahal Careers Channel, which provides a
List of Jobsites.