"You should read this book ! Oh, I am already reading this book "
I think that is the actual way :)
I think this is a case where there is no good direct translation - I think in English, we'd say "I have already started reading this book", not what the direct Duolingo translation gives.
The Hebrew sentence, אני קוראת את הספר הזה כבר, if translated word for word would be, "I'm reading this book already." Although it may be slightly more natural in English to say, "I'm already reading this book," neither sentence is wrong.
I was marked wrong for saying "I already am reading this book", isn't that the same meaning as the answer ?