Is copying an image from a previous paper of mine and citing its source considered self-plagiarism or unprofessional? Last year, I wrote a paper and it got accepted and was presented at a conference.

This year, I am writing a more in-depth paper about a similar subject; but since one of the figures in my first paper is adequate for my purpose, I want to reuse that one (of course citing it adequately).

Am I OK in doing that, or is that seen as self-plagiarism or unprofessional?
There is such a thing as self-plagiarism, but I would say that your case (reusing a figure that you created and providing a citation to it) is not an instance of it.  I also don't think it is unethical or unprofessional.  As Ran G. says in his answer, just make sure you ask permission from the copyright holder (if it isn't you).