after another attempt, I have managed to get the plugin working on my system.
My problem was a misunderstanding: I was expecting that the plugin to start the doxygen tool in order to generate the documentation output, something which the plugin does not do. After adding a build step to start doxygen, everything worked perfectly, even on a Windows slave.
So, sorry for the confusion, but I believe this is not necessarily obvious to a new user. The same probably applies to javadoc.
So, as far as I'm concerned the issue can be closed, unless other people are still having problems with this.