I was an au pair in Europe for a year. Before I arrived I spoke NONE of the language whatsoever. My DB knew English moderately well (but traveled often for work), my MB very little, and my 7 year old charge spoke no English at all. Once I arrived, I enrolled in language classes but my progress was incredibly slow :long story short, I was learning German but living in Switzerland in an area that speaks Swiss German which is a virtually unwritten language and varies greatly by village - therefore I wasn't hearing "high German" around me and once people realized I had an American accent, they simply spoke to me in English.
However, the 7 year old an I communicated fabulously! In the beginning, we had to be creative (drawing pictures, looking up words, using grand gestures and acting things out). And around three months into my stay, my charge was more fluent in English than either of her parents and often acted as an interpreter between MB/DB and I. Meanwhile, at around the same 3 month mark, I was still struggling to ask "where is the train station" in German.
Children have an incredible ability to communicate creatively and pick up on new languages.