Do I need an I-Q (in-phase/quadrature) mapper in Simulink with the QAM modulator?
You don't need the mapper. The Simulink QAM modulator lets you specify a vector of constellation points. The input should be an integer (or vector of integers) that select elements from the constellation points.

By default the block specifies a 8-PSK constellation. If you want something different, you need to provide the vector of constellation points.