As a native (S.E) English speaker there is absolutely nothing wrong with this sentence. "My money is gone"/"Dad will have taken it" appears to reflect upon an earlier conversation where you (as owner of the money) have discussed with Dad taking the money somewhere (the bank maybe?) If you are a lazy teenager and sleep in, you may find the money gone when you awake - hence the conversation in my example
My favourite fictional one on that topic is "You Stole My Heart, You Stole My Dog, But You Ain't Gonna Steal My Chevy". :)
This version of the English (dad will have your money taken) makes it sound as if dad is going to arrange things so that someone else will take your money. (Dad is going to see to it that your money is taken.) The original sentence (dad will have taken your money) makes clear that dad is the one who will have taken it.
There is something odd about the sentence, though, which is that it seems to be predicting the future (and not a in particularly nice way). Dad's such a cad that he's going to steal your money...... (and your guinea pig will die, and it will rain all week, per Arnauti). But that's not a problem with the grammar - it's a problem with the scenario!
In my experience, we would normally use this construction as a tentative way to say things - to soften the statement, as it were. "Dad will have taken your money" (that's where the money went...) it's a way of saying "Dad took your money" without sounding like a strong accusation (The last form sounds more like: Dad is a thief!)
This sense of the sentence is less likely in Swedish. Most likely this is about future events but reported as seen from a point even farther into the future. Like for instance, talking about events that will take place tomorrow, but seen from a perspective after they already happened. So it can answer a question like, "What will things be like next week?" Answer: "It will have rained all week, your guinea pig will have died and Dad will have taken your money." (sorry about that horrible prospect)
Actually you were right on my intent earlier. The sentence from the exercise by itself feels tortured; my example actually is something I might use, in (North American) English, so it is good to know that one doesn't do that in Swedish. Your example with that horrid week works really well, and is I'm sure much more widely applicable and helpful. (Poor guinea pig.)
This is a good point. The same construction is also often used to admit some uncertainty: imagine the sentence, talking at a time when the money has gone, to be the short form of "(I think it will turn out to be the case that) Dad will have taken your money".
Swedes might not use it that way, but Brits do.