Yes, things work differently for the object of a sentence (as you'll see in the accusative skill). BTW, I think daughter should be accepted for kız under any circumstances (a bit like in French fille can be both girl and daughter), so it's probably just a variation they haven't added yet.
This ia highly confusing by Duo. here they require you to write "The" everywhere, despite the fact that the turkish sentence does not have the. Later on they will intrdute the ending that will clarify where "the" is used in Turkish, but by that point you will think this is the correct way. Absolutely idiotic logic and very confusing.