I've never had anyone ask me what qualifications I have, and I don't advertise, so it doesn't really arise as an issue.
I started off teaching the daughter of a friend, who then referred me her best friend, best friend's mother and brother, friends of friends etc and things got started slowly but then grew by word of mouth.
If you want a general introduction to teaching, the Associated Board run several different introductory courses (look on their website in the teachers' section). I did the CTABRSM course after a couple of years of teaching and then the DipABRSM (teaching). I think those were both useful qualifications that actually taught me useful things about teaching, rather than being just a piece of paper.
The concern here is that you are entirely 'self-taught' and therefore haven't been exposed to any conventional teaching methods. It doesn't mean you won't be a good teacher, and to some extent I suppose you have to try it and see for yourself, but you could go a long way towards convincing me to give you a try as a parent by showing me some evidence that you know about teaching methods - have you read any books? been on any courses? How would you cope with a child who didn't "get it" when you tried explaining or demonstrating something - I learned the hard way that repeating things over and over and being incredibly patient isn't enough - you need to be able to spot problems and be able to deal with them effectively, understand how different children (and adults) learn in different ways - for instance, are you aware of the concept of visual/auditory/kinaesthetic learning? How would you go about incorporating aural training, theory, sight-reading, improvisation and so on into your lessons?