An OoO core with speculation has to be able to roll back arbitrary instructions when an earlier instruction causes a visible trap after a later instruction has been executed. Because of this, the core needs to be able to reconstruct the value of Q at any point of execution, even if it's not actually needed then. So the order matters.
Good point. So then instead of updating Q out-of-order you could update at commit. You just need to block any instruction that reads Q until the OoO core is empty. This is _much_ cheaper to implement than adding a dependency on all instructions.