Qualifications
Being über-bendy isn't going to cut it. To become a yoga instructor you need to get yourself certified. Many yoga studios offer training courses. Odds are your nearest studio does, and hopefully they already practice the same type of yoga that you want to teach. Each studio has its own preferred yoga technique, so you'll have to choose the studio you want to train with the most. Bikram? Hatha? Greek?
The most widely accepted certificates come from the Yoga Alliance; $3,000 (yikes) and at least 200 hours of training will get you your certificate. That little piece of paper will get your foot in the door at almost all yoga studios, health centers, and gyms. If your preferred place of professional posers is certified somewhere else, find that out before you apply—we don't think these places will want to refund your entry fee.
If you're really serious about making yoga your full-time profession, or are interested in higher-level management positions, a bachelor's degree in physical education or physical therapy is a solid choice. Physical and occupational therapists specializing in yoga therapy are in high demand (source).
This is also a great way to add some stability to your otherwise uncertain career. Think of it like doing tree pose for a long time, but by doing it you know you won't be standing in unemployment any time soon.