How funny, I was just researching this the other day. I'm going to my sister's pinning ceremony next weekend (which used to be a capping and pinning ceremony) and so I got curious and did a little reading on the history of nurses' caps and uniforms. The article I read was "Image, Function, and Style" by Lynn Houweling, published in The American Journal of Nursing. Really cute pictures if you have access to Jstor.
The transition from white dresses to scrubs for American nurses happened somewhere around the 1980s, but the roots of the transition stretched back into the 60s when hats became less and less common in women's fashion, and therefore little caps started to be seen as old-fashioned. There was also a push with the women's lib movement to put nurses and doctors on more equal footing, and the distinctive, highly feminine dress for nurses was seen as not advantageous to this. Apparently there was a brief period of white pantsuits being popular with nurses in the 1970s before the total nurse scrubification of the 80s. The 1980s, conveniently, was also when there was an increasing number of men entering nursing pretty much putting the nail in the coffin for highly gendered nurse uniforms.
In what country?