“Fursuiter” is a fairly old term, relatively speaking. Wiktionary lists two examples from 2009 and 2010, but I’m sure the term is way older than that. There’s an Urban Dictionary entry from 2003, for example. The Wikipedia article about fursuits says that the term “fursuit” is “believed to have been coined in 1993 by Robert King,” and adding the -er to it to describe someone wearing one feels natural enough for it to have happened soon after that.