It is the nature of the IO bonds that the experts argue over. Is it I:rarrowO (a dative covalent bond) or I=O, an Iodine oxygen double bond?
For undergrad purposes take it to be a double bond (each using two I valence electrons) the I:OH bond uses the remaining valence electron.
With this info you can draw a Lewis structure and hence the shape from VSEPR arguments. Unfortunately the structure of IO3(OH) has not been determined in the gas phase; in the solid state it is a polymer with I-O-I bridges.
[IrO4]^- is tetrahedral (cf [SO4]^2-).