如果我是你，我也这样做。

The grammar is correct but the translation is not right. What you wrote is, "If I were you, I would do this sort of thing." which is totally different from your original intent. "If I were you, I would do the same thing" = "如果我是你，我也<<会/同/一/样>> 去做" shiyichao's is just another way of expressing it.

如果我是你，我也會這麼做。

the same thing在汉语里有相应的说法“相同的事，同样的事，一样的事”等等。那么译成“如果我是你，我会做同样的事”是可以的。如果想译得更更自然一点，也可以译成“如果我是你，我也会那么做。” 我不会使用“这样”。

如果我是你，我也会做同样的事儿。