Again, I apologize for causing confusion. Here's for clarification:
With "doxygen tool" I meant the command line client. When I first tried the Jenkins doxygen plugin I was a Jenkins newbie, and I wasn't aware of the fact that I had to take care of invoking doxygen myself using a build step. So in that respect the error message was completely justified – the output directory indeed wasn't there, because I failed to run doxygen.
That's why I was saying, as far as I'm concerned, the issue can be closed.
What would definitely help newbies like I've been, is to have some sort of step-by-step instructions on how to set up doxygen with Jenkins. Ie first create a new build step to run doxygen, second tick the check mark for the doxygen plugin etc. etc.