Welcome to Flyertalk.

As you are posting in the CO Forum, I assume you and your family will fly to Germany on Continental. Call them up and ask them. It's possible to take pets on your Continental flight but of course they have to go into the belly.

You need to reserve space for them in advance and pay for it. Also, make sure you fulfill all the requirements necessary to import them into the European Union.

By the way: Two thumbs up for moving to Germany. ^^ May I ask where you are moving to?