The short-time dynamic behaviour of the two-dimensional classical Coulomb gas of half-integer charges on a square lattice is investigated using Monte Carlo simulations. We estimate the second-order phase transition temperature T _c and all the dynamic and static critical exponents z, β and ν. The value ν 0.77(2) obtained is different from ν 1 in the pure two-dimensional Ising model, which provides evidence of a non-Ising exponent in the charge lattice melting transition. In addition, the dynamic critical exponent z is found to be 2.01(3), which is also different from the z 2.165(10) accepted generally in the pure two-dimensional Ising model.