Doulas are yuppie stuff in the US, mostly. Also connected with home births to a large degree, rates of interest in which I'd expect are also connected with income, to a point. I'd definitely bet most US fathers wouldn't be able to tell you what it means, though it's possible that a majority of fathers on this site know the term (I did—but then, of course I do).
I'd be interested to see how knowledge of a lot of these words breaks down by income. (I too know what a doula is; I'm not sure if I knew this before my partner was pregnant. We did not use a doula, but we're of the class of people who at least think about it.)