I, as a native English speaker, would also say this sentence without "on" at the end. Its quite awkward that way.
Me to! I know what the system wants to read, although many English speakers are not convinced by the strukture of this sentence.
Just another tought. Danish is closer to German than to Englisch. In German we would say: Mein Bettzeug ist blau mit Elefanten drauf. That is the 1:1 meaning of the Danish sentence. We will probably have to live with the fact, that some few translations, Danish to English, will remain a little bumpy.
As a native English speaker i would not use this sentence with on at the end.
So far it still counts you wrong if you do not put "on" at the end. 5/2/17
I grew up in Minnesota and the English translation actually makes sense to me... ;)