I'm just beginning my career in the music industry aswell. I have taken lessons in several instruments in the past and a my dad runs a guitar tuition business full time from home. I have considered instrument tuition myself but my passion lies in artist management which is what I'm now pursuing.
The main thing that prevented me from starting my own teaching business was not having the space to teach (of course with a guitar you have the option of teaching students in their own home if you don't have your own space...this is not so easy with a drum kit)!
It also helps to be qualified. Apparently being a grade 5-8 in your instrument is about the right standard for teaching. You can also take courses specifically in instrument tuition if you want to take it seriously.
I believe the most important thing whatever aspect of the music industry you are going into is networking! Talk to and get advice from as many people as you can. I set up a couple of meetings with my drum teacher initially who gave me some great advice on getting started and showed me how to make lesson plans etc.