> The argument is that subjective experience would not have evolved without free will.
That's not an argument, it's an assertion. By its nature, subjective experience can't be used as an argument, because it's not accessible to the other parties to the debate. This is how subjective experience is defined.
> If there's no free will, then an animal with subjective experience would not have an evolutionary benefit over one without it.
This is easily refuted by examples in which computer programs, neither conscious nor possessing free will, without any behavioral latitude whatever, in a rigidly defined computer environment with no random or unpredictable elements at all, evolve according to the usual rules of natural selection. Therefore evolution and the existence of natural selection cannot be used to argue in favor of free will.
> Is my argument for the existence of free will correct?
It's not only not correct, it's not, strictly speaking, an argument. This is not to say there is no such thing as free will. We just don't know.
The evidence for an argument in a debate must be accessible to all participants in the same way. This is not to say they will agree with the premise, but they will all experience the evidence in the same way before drawing their own conclusions.