It sounds better. You could be able to get rid of the "que" by saying "Peut-être devrais-je étudier l'allemand". That would be correct, and a more elaborated sentence as well.
You can consider that everytime you see "Maybe I..." you translate it as "Peut-être que je..."
It's a remnant of the original meaning of peut-être: "Il peut être [= il se peut] que je devrais étudier l'allemand." With an impersonal personal pronoun il as in il faut.
Very hard to understand what she's saying - sounded like également not l'allemand to me!
There's a real inconsistency with translating "devrais" as "I should" vs. "I had to" in these exercises.
Are there any good links/articles explaining the relationship between the 'must' and 'should' uses of 'Devoir'?
There are a lot of examples here: http://www.larousse.fr/dictionnaires/francais-anglais/devoir/24917
And a great explanation here: http://french.about.com/od/grammar/a/devoir.htm