Translation:She will book a trip to Copenhagen.
In addition, all of the other exercises that I've seen in the lesson accept "shall" as a translation. I think it's a fine memory trick (ska-skall-shall) for English speakers learning Swedish, even if it would cause problems for Swedish speakers learning English. For these reasons, I'm still confused why "shall" wasn't an acceptable answer.
Harold, you seem very fond of pointing out that you're a native speaker. Surely you are aware this does not mean you have heard all regional variants of English. I assure you that the phrase is in actual use, even though - like I stated - reserving a ticket is more common. Or a place, as you correctly mention.
Yes - and no. For instance, Americans may be unaware of British idiomatic expressions, and vice versa. Your input on the native English with which you are acquainted is very welcome and highly valuable. Dismissing the English of other native speakers because you hail from a different region is not.
Always interesting to find out nuances of meaning that vary in different English speaking communities. For me reserving something means you haven't actually booked it yet - e.g. You can reserve a trip without paying anything (or sometimes a nominal admin fee) and they hold the place only for a certain number of days so that no-one else can book it in the meantime but once that period is over the place you reserved is freed up again for someone else to book. But when you pay (sometimes x% of the total) for the trip, you have booked it - it is then yours right up until the departure date and no-one else can book it.