With regard to which is right: "breastfeeding" or "breast feeding" (or
"breast-feeding"!), I run across similar questions all the time. And, believe
me, everyone has their own point of view, which they strongly defend! The
pattern in the ongoing evolution of the English language is this: when two
words are frequently used together, they soon become hyphenated, and in time
they end up being one word. This is the "rule" followed by most Canadian
and U.S. editors. I don't know about the rest of the world, but I assume the
British and Australians follow the same rule. So I'd say that "breastfeeding"
is the way to go!

Andrea C. -- science writer/editor, Victoria, Canada