Emulating Q is not strictly necessary. Only a 1-bit flag, indicating whether the previous instruction computed flags, is needed to emulate the behaviour of SCF/CCF.
Also note that while POP AF and EX AF,AF' modify F, they do not compute new F values. [https://github.com/hoglet67/Z80Decoder/wiki/Undocumented-Flags#scfccf Source]
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| IR (Instruction Register) || 8-bit || Holds the opcode of the currently executing instruction || Internally used, not accessible by the programmer