I'm looking for a terminal emulator that does the same thing as
konsole, except written in Java.
I have used Java Telenet - a terminal emulator that can be embedded in a web page and thus constitutes a zero-install application (assuming a JVM is available)
Google finds many, including JTA a Telnet and SSH client
JediTerm is VT100 compatible and has implementations to work both for ssh connections and local pty.