To the chain of development of 2D materials, recently synthesized ultrathin cobalt oxy-hydroxide (CoOOH) nano sheets gain potential interest due to its structural, electronic and other properties. We have studied the interaction mechanism of two toxic gases hydrogen peroxide (H2O2) and ammonia (NH3) adsorbed over 2D CoOOH to understand the role of 2D CoOOH as a toxic gas sensor. We employ first principles based dispersion corrected density functional calculations to study the sensing behavior of 2D CoOOH towards H2O2 and NH3 by calculating adsorption energy, electronic band structure, density of states (DOS) and work function. The electronic band structure, DOS and work function of 2D CoOOH are modulated after adsorption of H2O2 and NH3 molecules. Adsorption of gas molecules confirms the sensing behavior of 2D CoOOH towards these molecules and depicts its use in a sensing device. The full phonon dispersion curves and phonon density of states reveal the dynamical stability of 2D CoOOH. The calculated adsorption energy of H2O2 and NH 3 molecules is - 0.532 and - 0.460 eV respectively which indicates the strong physisorption of these gases over 2D CoOOH. The ultrafast recovery time of 1239 and 1203 ns respectively were found for H2O2 and NH3 on 2D CoOOH. The work function which is 6.29 eV found for 2D CoOOH, decreases to 5.63 eV for H2O2 as it follows the reduction process on 2D CoOOH, and increases to 6.44 eV for NH3 molecules as it acts as oxidation gas on CoOOH. Our study reveals that the 2D CoOOH can be a better sensor for the H2O2 and NH3 gases than some traditional two-dimensional materials.