My first thought was an ER collet, although 18 SWG is only 0.048" diameter, just a little over 1mm (1.219 mm if you want be more precise ) So ER 12 or 16 would seem the more obvious choices, rather than ER 20 or Er 25. Unless you envisage the need to hold larger work, in the future.
Jason's suggestion of a small drill chuck is a good, and cheaper alternative to buying a ER collet chuck and collets; although they will always be useful at some time in the future.
Using a drill, or collet, chuck allows the work to be done in the lathe, even if not under power. It should keep the thread on the centreline of the brass rod. This should minimise the chances of ending up with a drunken thread.
Howard