In American English, child care is two words when it functions as a noun phrase. It’s usually hyphenated—child-care—when it functions as an adjective. For example, we might write, “I need to find child care, but child-care costs are expensive.” But American writers sometimes use the one-word form—childcare—as the adjective.
In British English, childcare is almost always a single, unhyphenated word, even when it functions as a noun. So the same sentence would be, “I need to find childcare, but childcare costs are expensive.” British English tends to lead the way with certain compounds, so we can expect this form to catch on more broadly in the next few years.
For now, the two-word form is more common in Canadian publications. Australian and New Zealand publications favor the one-word form.
We base all of this on Google News searches covering the last few years and limited to the websites of large news organizations with editorial departments. Spelling habits might be different outside edited newswriting.
These examples from British publications reflect the trend of using childcare as both a noun and an adjective:
Yet we were told even by leading feminists that caring was work in a care home but not in our home, and that childcare was a job like any other. [Guardian]
The Australian backpacker, who is believed to have limited childcare experience, registered with an au pair agency. [Telegraph]
[E]mployers introduced practices such as flexible working, job sharing, and on-site childcare, or crèches. [Financial Times]
American publications tend to use child care and child-care—for example:
In a parallel universe where high-quality child care was free and my dream job required me to work outside of the home, would I choose the same path? [New York Times Motherlode blog]
Beal graduated in December with a bachelor’s degree in psychology and is now a child-care worker at two group homes. [Los Angeles Times]
The central bank attributed its revised inflation forecast to government steps such as the expansion of child-care benefits and free school meals. [Wall Street Journal]