No idea, Andy, but there are several places incorporating the name, some "an der Iller", names listed here -
http://www.geonames.org/search.html?q=Iller&country=DEThis suggests that to me that it's more than just a stream. A map I have shows the Iller running through Ulm, and south of Ulm there are settlements with names like Illertissen, Illerberg, etc. If the age of these settlements could be determined (wikipedia?) that might give an early date for the "stream" or river name.