lookup table using vhdl:

For two bits IQ mapping, you only have 4 IQ points (QPSK) hence one +/- amplitude level per I or Q. you don't need to worry about sqrt(2) since all levels are same and you can choose any high enough +/- value that suits your resolution.

for multi-level case e.g (16 QAM), you have at least two levels and then you need to scale amplitude according to constellation diagram(ratio). But this is not what you are after.