As an earlier comment (How can a research mathematician transition into a mathematics education researcher?) indicates, I speak from the perspective of someone who has done a smidgen of math-education research, but not in any sense as an expert.
With this caveat, I think that it is important to realise that math-education research is much closer to science research than to math research, in the sense that it is necessarily an experimental science. As such, gathering experimental data is research, and this is something that we do every day, as teachers. (I believe that the usual term for this is 'practitioner research' (https://en.wikipedia.org/wiki/Practitioner_research ).) This is not the only kind of research that one can do, but it is a legitimate and valuable kind, and it is one that is accessible to you with only a little bit of extra training.
I have heard a math-education teacher literally say "I had an interesting experience in class today. I wrote a paper about it." While I am not sure that this is the kind of mentality that one should seek, it at least shows that writing a practitioner-research paper is not necessarily the huge and time-intensive process that writing a mathematics paper seems to me to be.
I also strongly recommend working in concert with an existing math-education researcher, collaborating informally (discussing ideas together) if not formally (writing a paper together). Such a person will be able to tell you whether questions you have are interesting; to suggest ways to elaborate on, expand, and research them; and to advise you on how to write up results or discoveries that you might find. (A tip: don't try to transfer your knowledge about writing mathematics papers directly to writing math-education papers. The latter are much closer in structure (I think) to papers in the social sciences.)