You're not officially "Qualified to Teach English" unless you have a teaching qualification that says you do.

In Jiangsu, China, my visa manager tells me you must have a bachelor's degree, a TEFL certificate, and at least two years post-grad teaching experience. (The latter may soon be relaxed - waiting to hear.)
Also, unless the person has a Jiangsu-issued visa and work permit, they have to leave China and reapply, making getting teachers even more difficult.

As I understand it, different parts of China have different interpretations of the 'guidelines', depending on local economic and other factors. You may, therefore, find a job in China where you can be employed.
However, China has a difficult market to negotiate. There are agents and companies that will outright lie to you, or cheat you.

Be wary of "Travel and teach" offers. I've come across foreigners who were sold the idea of travelling to China and teaching as some sort of "holiday travel" or "community help" basis, accepting low wages for full-time positions, only to discover the agent has pocketed most of the salary as commission; essentially tricking the teachers. They have found themselves in a school with teachers earning far more for the same job, sometimes working illegally.

Look around, and use your own judgement on the quality of the information you receive. Like anything on the internet, more than in real life, trust nobody until you are absolutely sure!

David.