No, it's not wrong. It's in fact almost the standard view, but there are also more confusing views, especially when you throw "contrast", "emphasis", etc. in to the mix.
That's the way I understood the subject/topic in Japanese.
Subject -> 富士山が高いです。
Topic -> 富士山は高いです。
Is that wrong?
As I said above, alice313, "subject" and "topic" are still very confusing in Japanese, so I'm NOT going into this direction but just pointing out that since "私はうなぎにします" is a full sentence, then you'd be better off to take "です" in "私はうなぎです" as a (pro-)form of "にします" in a context where the information is so clearly understood that the original form doesn't need to be spelled out in full. So, "I am a eel" is only a joke and no one would argue seriously about it.you'll be asked "何にしますか？" and you can say "私はうなぎにします", or "私はうなぎです" if some of your friends already finish their ordering.
In this situation, "私はうなぎです" doesn't mean that "I am a eel" (Subject) but means, "about my choice, I'll order eel" (Topic-about~).