Caricatura, dont be put off about starting an 'art school for kids' because you are as you say an 'alternative artist'. If people are going to send there kid to an art school, maybe they want what is different, what they cant easily do at home or at kindy/school. Dont let that put you off.
You need to do a business plan -get serious and research! Research other 'art schools' for kids that are all around your country/town/city and even overseas to get your 'business info' together. You will have to 'budget' out your projects to cover costs and charge for your lessons. An average 2hr lesson can be $10-$20 depending on type of mediums used, age group and how long the session goes for.
Aim for a minimum 5 students. If they are really young them parents have to stay. No more than 8 depending on age.
Research funding -small business start up grants, or art community development grants.
Survey your community -get an idea what they want, how much they are willing to pay, when is convenient for them e.g. 3.30-4.30 after school, during school hours for 3-5 year olds etc etc
Start thinking, writing down ideas. This will help YOU immensely. If you are clear in your mind what you are doing then it will all come together. Start off with a basic 4, 6 or 8 week course.
This is an arts franchise where I live http://www.theartsemporium.com.au/