This expression seems to be mainly written as
call girl, and sometimes as
call-girl. But, as you say, Les, the Macquarie has it as
callgirl. And Wiktionary gives the single-word version as an alternative spelling.
The one-word version is sometimes used in publications, such as the 2004 book
Callgirl: Confessions of a Double Life, by Jeannette Angell. Or in this 2011 rant by David Thomas in the
Daily Mail:
But to earn respect one must first look like someone who deserves it. This isn't just an issue for teachers. It applies across the board, from doctors in jeans to policemen in baseball caps; from vicars who dress like tramps to newsreaders who dress like callgirls. Britain has become a shabby, demoralized nation. It's time to smarten up.
Callgirl will be allowed from now on, as a rare word.