We passed our first (of five) Danish language tests!
We are now officially DAS students (Dansk er en Anden Sprog, or Danish as a Second Language). I now feel comfortable telling Danes: "Jeg kan ikke tale dansk. Kan du tale engelsk?"
In theory, we can carry on more complicated conversations, but all attempts so far have been disastrous. We walked into our local pizza place, and asked the man behind the counter, in Danish, for "a Number 9 and a Number 35." The man walked off, and came back looking confused and speaking in rapid Danish. He didn't speak English, so we just stared helplessly. Eventually, another man in the restaurant explained that you should normally call with your order before walking in to pick it up.
We have had similar experiences in grocery stores, bakeries and the library. As pathetic as it is, it seems the best option is just to answer questions with "Sorry, I don't speak Danish." Hopefully, the situation will improve as we plan to continue taking Danish classes for the rest of the time we're here.