"With a cat."
I agree, short sentences help you clearly work out how German works (I'm currently seeing "ja wohl" in lots of long sentences and have no idea what it adds to a sentence) I'd find this stuff helpful:
short sentences like "the dog is eating" and "with a cat"; they make longer but similar sentences like "a dog is eating lunch with a cat" seem far less daunting. Perhaps structure lessons to begin with shorter sentences and end with longer ones
lots of simple sentences like "mit einem Hund" "mit einer Katze" which show how the words change based on German grammar
a short grammar tip at the bottom telling you why you've written articles, verbs etc. in a certain form - even if you haven't gone wrong - would be really useful (e.g. "use the ending "-em" for masculine nouns in the dative case)
I had a pretty good German vocabulary before I started Duolingo. But not a very good understanding of grammatical structure. The longer sentences are fine once a concept has been introduced. But a new concept needs to start simple. I really struggled with the Dative lessons until I hit "mit einer Katze".