You can go over for a while as an au pair - but be very careful there. The US doesn't have much if any regulation over the "au pair" job title. In most of Europe there are limits to your working hours and duties, plus you have to be given time off to take classes. None of that in the US - and most Americans refer to their "au pair" as a "nanny" - and expect someone who takes care of the kids, does all forms of housework and functions as a general dogsbody.

You might look into some sort of job exchange program. CIEE was always the major one, though a quick look at their website indicates that they seem to be focusing these days on foreign exchange opportunities for Americans. Still, it will get you over there for a year or so, and you can decide at that point where the relationship is heading.
Cheers,
Bev