Perchloric acid is a strong acid, and thus it will dissociate completely in water. Therefore you don't need to use Ka to calculate [H+]. For hypoiodous acid, a weak acid, the Ka determines the extent to which the acid ionizes. Here you use the given pH to calculate [H+], and using an ICE table you can calculate the concentrations of the other species in the solution.
The 10-14 rule only concerns the relationship between an acid's and conjugate base's Ka and Kb values. To use the 10-14 rule, you'd be concerned with [HIO] and [IO-], or [H+] and [OH-]. You can't mix and match acids and conjugate bases there.