By analyzing the compositions and concentration of dissolved gases in power transformer oil, it is possible to effectively identify and predict the types and degrees of internal faults in oil-immersed transformers. This technology is currently an important method for fault diagnosis and prevention of large oil-immersed power transformers. This study established two different adsorption systems, namely Ti3C2O2 and Ti3C2O2 doped with Au atom, for the detection of four fault characteristic gases (CO, CO2, C2H4, CH4) in power transformer oil. The research results indicate that Ti3C2O2 exhibits inadequate adsorption capabilities for the above gases. The maximum adsorption energy is only −0.440 eV, which belongs to physical adsorption. After doping with Au atoms, the adsorption sensitivity of Ti3C2O2 for the above gases was significantly improved, with a significant increase in adsorption energy and charge transfer. The average adsorption energy has increased by 435%, and the minimum adsorption energy is also −0.660 eV. The adsorption process changed from physical adsorption to chemical adsorption. These research results provide a theoretical basis for Au-doped Ti3C2O2 gas sensor in detecting fault characteristic gases in power transformer.