I'm trying to use the JDK 11 compiler with DrJava, but there is no setting that allows me to change it. I've downloaded it from Oracle and installed it on my machine, and then downloaded DrJava. There's only the JDK 8 compiler that appears in the list.
According to the DrJava documentations, the current beta version (drjava-beta-2019-220051 that's what did you download probably) is compatible with Java 8, which is the only supported version of "traditional" Java. Later versions of Java use a new package system and distribution format breaking compatibility with Java applications that access files in the underlying distribution.