Why the ionization energy of Au is more than that of Cu?
Smaller size does not necessarily correlate with higher ionisation energy. The trends in 1st IE going across Period 2 offer a simple counterexample.

A better (but not 100% foolproof) guideline is to use the orbital energies (see: Koopmans' theorem). The higher the energy of the orbital from which the electron is removed, the lower the IE.

In the case of gold versus copper, the first ionisation corresponds to the removal of a 6s or 4s electron respectively. In gold, the 6s orbital is relativistically stabilised, leading to a larger than expected ionisation energy. See also Geoff Hutchison's answer here.