Your DS-2019 Form needs to be signed for travel validation in order to travel outside the US (example: mexico or canada). you should have received it during your training in New YOrk.
And...ALWAYs check the website (google search) for the country to which you are traveling to see if there are any additional visa requirements.
It is YOUR responsibility to check for additional visa requirements, not your CC's and not Euraupair's.
Here are links to the websites of popular au pair desinations during the program year: